No, most absorption RV fridges(the kind you have, that can use propane) use
12v DC for the controls no converting AC to DC. They use AC for cooling power or propane for cooling power and a small percentage can also use
12v DC for cooling power. With this you would need to turn off
12v DC to reset controls.
The newer compressor fridges use 12v DC or 120v AC for cooling, no propane. Many of them actually convert 120v AC to 12v DC so really only cool with 12v DC. I believe they also will not run without 12v DC for the controls, not sure since I don't have one.