Agree with Frank. Unless you are going to use the fridge in a week or so I would turn it off. The useful life on these RV appliances are pretty terrible so less hours on them the better. I always shut mine off and prop the doors open so they dry out. I live in So. Cal and no humidity so it dries out fine on its own.
Plus you will just consume propane while in 12v mode and while it doesn't use a ton of propane compared to a hot water heater or furnace, it will still be consuming something you will have to fill sooner than if you left it off.