Does city water hookup keep hot water full on Jayco 1207?

Except Jay Series 1207 is even simpler, with no toilet, no shower, only one sink, and no wastewater tanks. ;)

Roy, that is an excellent diagram!

This is a simplified water flow chart for a typical trailer...

Yes, camper water systems are set up to feed everything from the city connection -- some people never fill or use the fresh water tank at all.
The water heater is plumbed downstream from the point where the pump and city supply lines tee into. This means the heater will draw from whichever side has pressure.

However, there are valves in the system used to isolate the hot water tank so it can be drained for winter, etc. These are most likely oriented correctly so that you can switch back & forth between tank & city without worry.
You should however familiarize yourself with the plumbing layout. There should be schematics in your manual, but it is also worthwhile to take a good look at the plumbing and follow all the flow options with each valve setting and water source.

You'll be fine:)
The city connection will pressurize your system (including the water heater)...just like at home.
The gravity fill is to fill your tank, which in turn, has it's own pump, to pressurize the water system.
There is a check valve (one way flow) to keep water from going into the tank (when using the city connection) or out the city connection (when using the water tank/pump.

Note, just make sure that your water heater is full, before you turn it on, or you could burn it out. You can check by flipping the little lever on the Pressure release valve on the outside of the water heater.

Enjoy your trip.