Welcome to the forum... where there are no dumb questions.
You can leave the pump turned on while connected to city water if you like. It will kick on if your pressure drops below it's threshold and supplement your flow from city water by drawing water from your tank and bumping up the pressure a bit.
No problem either way. You just don't want to have it turned on when you're filling your fresh water tank since that causes an issue on many rigs.
Rick