You can find out easy enough by just turning on your 12v
water pump and then looking around outside the trailer for water coming out somewhere. Listen for your pump to stop when it reaches its pressure setting.
Almost all Airstreams have a check valve to prevent water from exiting the city water line when using the pump. Many regulators won't allow back flow thus acting like a check valve. Many 12v
pumps won't allow back flow so you won't fill your fresh water tank while on city water.
But since your trailer has two "pressure sources"; city water and 12v
water pump, you need to isolate them with a check valve of some sorts so it's "either city water OR 12v pump".