Railroads and City-States

In my current game about a third of my empire is on the other side of a narrow 1-tile isthmus that has two large seas on either side that a city-state is sitting on. The city-state is allied and my city connections pass through it.

However, now that I have railroaded my empire I've noticed the city/state is still labeled "road" and I'm not getting the 25% railroad production bonus in 1/3 of my empire.

Will the city/state eventually flip to being a railroad?

(I don't want to take out the city/state since it's culture and I am like 220/60 friends and I'd have to wage war with two friendly civilizations to make harbor connections on the seas.)

Yes, City States advance technologically, based on I think the average research.. so you'll just have to wait until it gets Railroads. upon which it should become a Railroad City.

I've noticed that Harbors provide railroad connections, so if you put a harbor in a city on both sides, you should get the railroad bonus.