Yes, turn off the city (aka shore) water. If you've got some water in your fresh tank, that's great. With that water, you just turn on the on board pump when you need water, turn if off afterwards to minimize the leakage as I assume it's a pressure leak. With no pressure on the system from the city water, the leak will likely slow to a stop when you shut off your pump. When you need more water, just add to the tank.
You can go weeks...months...using your on board tank and pump ONLY WHEN YOU NEED WATER and shutting it off later. And likely, the leak will be slow enough that it won't do any damage. Put a plastic tub under it if you can.
When you get home, then work on it. Don't let a little leak spoil your vacation.
Of course if your leak is from the fresh water tank itself, you'll have to do something. But usually that's not the case.