Most likely would not be used

Most likely would not be used in day to day operations.  

Maybe they would use it for special weekend runs. 

Or part of a museum display. 

Is it a freight motor or passenger?

Freight could possibly be used in MOW service. 

The prototype I can think of similar to this scenario.

As I think about it, I may have a prototype example of such services used in real life, being the New York Subway and how they run historic train cars sometimes, it could be possible that the city transit company does the same.  How often does the NY train run?

Liberty Bell

Ah the terrible question.

Depends. It operates a a single car so it wouldn't have a high capacity, it only seats 25-30 people, so isn't designed to be a mass transit type car (which can accommodate 6-100 people per car and are typically run in sets).  They also would not meet current handicap access requirements.   The Liberty Bell cars were intended to be a "limited" car, a car that was a higher class and made fewer stops than a typical  car and were run on lower volume branches.  They could operate from both street level and high level platforms and were equipped to operate on both trolley lines and third rail lines.

To answer your question, I would say, no.  They would be suited to a low volume branch serving a more suburban, commuter type operation where they are more of a limited service, higher cost service and where a nostalgic car would be more fitting the service.

Or a trolley museum.

As an aside, I used to live near Norristown and one of the routes I used to commute to college was the P&W line (the "Pig and Whistle") which was the route those cars used to get from Norristown to Philadelphia.   All the LVT cars were long gone by the time I started riding it.

It was an all third rail route with elevated platforms at the stations.  The platforms were maybe one car long, some only a half a car.  The terminus at Norristown was on the 2nd or 3rd floor of a drug store and it ran over a high trestle to  Bridgeport, where it went to ground level and ran at ground level all the way to Phillie's 69th St Terminal.  At that point passengers go off and go on the El (later subway) or transferred to various trolley lines.  The line operated mostly single cars, but did briefly operate the former South Shore "Electroliners".  The line was double tracked the whole way with third rails down the center.  It was very twisty and turny.  A friend of my described it as like riding a rat down a drain pipe

Philadelphia and Western Railroad - Wikipedia

Here's a couple "Bullet cars" on the approach to the bridge over the Schuylkill River near Norristown.  I rode these types of cars all the time, but since I mostly rode them off peak, they operated as single cars.  Note the curves in the track.

Other Prototype

I remember that in San Francisco (and I think somewhere in Europe) there are 1920's streetcars earning their keep in daily revenue service, with street cars from all over the place. Then there's also the Canal Street line in New Orleans, which is still running daily.

A good example

I may look some more into those examples of yours, as they may be perfect to work as an example of where such services are done

The car series

Well, the car series that my car is would be of the Liberty Bell Route 800 series.  It does not appear to have any pickup shoes on the bogies either.  As for the “High line”, it is running on one side of the city, but not the others, so it could be possible that the car would have a few stops on the line as well as a few in the surrounding areas

Prototypical?

As with all things, asking whether something is prototypical is different from asking how do you do something.

Two different questions, two different answers.  If you ask can I run this car prototypically in a modern transit system, the answer is probably no.  If you ask how can I run this car there are lots of options (they just might not be "prototypical".

For example in a modern transit system they rarely run trolleys anymore, they run pantographs, different type of overhead wire arrangements.  Places they run trolleys in a modern system tend to be more touristy type areas and less mass transit commuter oriented.

At the end of the day, its your railroad and you can do whatever you want, your layout isn't "prototypical" anyway, its totally made up so you aren't constrained to be prototypical.

Prototypical?

As with all things, asking whether something is prototypical is different from asking how do you do something.

Two different questions, two different answers.  If you ask can I run this car prototypically in a modern transit system, the answer is probably no.  If you ask how can I run this car there are lots of options (they just might not be "prototypical".

For example in a modern transit system they rarely run trolleys anymore, they run pantographs, different type of overhead wire arrangements.  Places they run trolleys in a modern system tend to be more touristy type areas and less mass transit commuter oriented.

At the end of the day, its your railroad and you can do whatever you want, your layout isn't "prototypical" anyway, its totally made up so you aren't constrained to be prototypical.

Yeah.

Yeah, I’m very pick and choosy about what I do prototypically and what I don’t.  Most of the fleet of my primary railway, the White Lion Railways, is electric and military equipment.  And we are based in the United States 

What About New Orleans?

Haven't classic 1920's streetcars been running in New Orleans forever? 

Or at least since the 1920's, when they were built..

http://www.norta.com/Getting-Around/Our-Streetcars 

https://en.wikipedia.org/wiki/Streetcars_in_New_Orleans

I knew about the New Orleans cars

I just didn’t know they have been running since the 20s

Trolleys

New Orleans has had trolleys since the 1800's (as had many cities).  

The trolley lines were built in the later half of the 1800's and generally lasted into the 1960's when cars put them out of business.  They were rediscovered in the 1970's and 1980's and some lines were rebuilt as "Light Rail Vehicles" (LRV's).

At one point in the early 1900's you could travel from Washington to Boston by trolley without having to walk more than a couple miles to change systems.  Pretty much all of that is gone now and they only operate LRV's in major cities.

Rockford

The closest thing I know would be Rockford's Park and Rec trolley car that still shares tracks with the UP

http://www.trainweb.org/chris/12rocktrol.html

-Matt 

Wouldn't work in your context, but...

Hi,

as for running outdated equipment on isolated lines, I know of some example...

In the outskirts of the city of Berlin (which has a modern tram system), there are a few small lines. They serve eccentric, small communities and have done so ever since the lines were built. Also built for recreational access to some remote corner.

One of those lines was running old equipment long after it was replaced on the rest of the system - the tracks were just that bad and none of the newer equipment would be risked or could even run on the tracks. The line has since been repaired but is still run with the oldest equipment that is available in the system.

Another line is operated not by the transit company but by a volunteer organization. They made it a feature to run the old vehicles - apart from the fact that the line is not connected to the rest of the tram system. Which makes replacing the vehicles or even running to the main depot for repairs unpractical.

Yet another example is a recently built subway line, which consists of only 3 stations and is supposed to be connected to the rest of the system "later". When built, a single set of subway cars was put in via the tunnel building access. Which has since been sealed to make space for the buildings put above. The longer it will take to build the rest of the line, the more outdated the equipment will be on that line. (I don't know about the current status of that line, it just isn't that important.

I'm sure you can find more examples of a similar nature if you look into it. While large transit companies don't like to run "non-conformant" things, there are some reasons for doing so anyway. However, you'll need a reason, for example an influential politician living exactly at that line...

Have fun and stay healthy

Some options.

TriMet in Portland Oregon actually owned small fleet of “Vintage” Trolleys. They were built new, but were based on a vintage trolley design. They were used on the system for special events and they facilitated charters. 
https://en.m.wikipedia.org/wiki/Portland_Vintage_Trolley

One of these Trolleys now operates as the Willamette Shore trolley with a self contained power car, diesel generator on a small cart. 
http://wst.oregontrolley.com/

Astoria Oregon also is a host to one of these wireless trolleys. 
https://old300.org/

SF Muni F Line

Juxen mentioned San Francisco. The SF Muni F Line has an operating* fleet of vintage Peter Witt and PCC street cars. The F (Market & Wharves) Line and runs through the main business and tourist areas.  Here's a link: https://www.sfmta.com/getting-around/muni/historic-streetcars

Lou in California

*SMMTA isn't running the vintage cars running right now due to COVID-19.

If

G'day Greenstar,

If your trolley route has been de-wired at some point past, use a generator car attached to your interurban car to supply the needed "juice" . 

The tramway museum at Launceston in Tasmania faced this problem and got around it by running with a generator car. See below for inspiration

That video is only a few weeks old. 

Also Melbourne is using W class trams (design dating from the 1920's) in daily service for a Hop-on/Hop-off service for tourists (and the locals use it too) on their City Circle route. The W class is one of the heritage trams operation on the San Francisco Muni tracks. It is possible that 1920's tram designs are still running 100 years in "service" after the first of the design was rolled out of the workshops.

late edit - Just found a Youtube showing that Milan is still using 1929-design single-unit trams in regular service, So they are out there for inspiration, you just have to get inventive,

When the city was built

Well, the story of the Megacity is that it wouldn’t be finished until about 2019 give or take.  And by finished, I do mean people would be allowed to move into the city.  It was built as a co-op by world governments to try to figure out a solution to making one of the greenest cities in the world, and is full of really tall buildings that are mixed use, including residential and commercial zoning.  
the interurban car in question would be given to the city, or ran solely in they city by the White Lion Railways for some reasons, possibly as a “nostalgia run” here and there.