There are several different types and models of Refrighrators used in RV's the most common is an Absorption Cooling Uint and works on what I call teh Ammonia cycle. This type can run on any heat source including but not limited to: Propane, 120vac and 12vdc (in some cases)
Most common is the propane/120vac (But the comments apply to 12vdc power too)
Now, in this category they come in two flavors Automatic and manual
An automatic "fridge" senses the 120vac, if it's present then it turns off the flame, and turns on an electric heater element. Since a heat source, to the cooling unit, is a heat source, it works.
The manual type you have to physically turn a switch or control
IN researching them I recently found there are two kinds of absorption cooling units, one uses a constant heat source (If on propane the flame burns till it is cold enough) the other uses a pulsating heat source (The flame cycles on and off during the cooling cycle,, I do not know if a unit of this type has EVER been bolted into an RV)
But for your question that does not matter.. All that matters is that be it a Propane flame, or an electric heat element, a heat source is a heat source