You have to have the switch INSIDE your rig turned on to use the propane. It allows 12v to get to your water heater to run the control board and the ignitor when using propane.
The switch outside turns on the 110 to use the electric heating element. If you're using propane, the outside switch should be in the off position.
Or... if you want to heat up your water quickly between showers you can run both the propane AND the electric element both at the same time.
So yes. You don't have to have the gas on when you're on shore power.