What happens is you get a bit more flow.. Well, at least in my trailer that's what happens... ;)
The check valve in the city water connection keeps you from pumping out water when it's not hooked up to the hose if you turn on the pump.
In the old days, you had to screw in a PLUG to the city water connection to block the water pump flow..
Today, the check valve does that for you..
If you are connected to city water and have the proper pressure valve attached you should only have around 40-45 lbs of pressure to the trailer. That's about all the pump provides too.
If you run 'both', you won't be pumping 90 lbs of pressure thru the system... ;)
It'll still be the 40-45 lbs as always, but you'll be pulling from the tank and the city water too..
Again, at least that's how it works in my trailer... :)
Mitch