I'm not sure how it works on the newer fridges, but on our old one, once the thermocouple kicked in, the 12V igniter turned off. If the flame blew out, the igniter kicked in again until the burner re-lit. On the new RV, I cannot hear the igniter clicking, but the indicator light blinks orange until the gas reaches the fridge and then goes green when it lights.
So basically, I don't think there is any 12V power drain from the fridge when operating on propane.