when you turn on the fridge to "gas", the interior light and thermostat control board on the fridge is operated by 12v power (and any fans that may be installed).... which is a low drain, but still a drain on the batteries...
if you have the refrigerator set to batt/12v operation, the COOLING unit will use a high volume of current while the unit is in "cool down" mode, and drain a 100amp battery in a day or less....
when on AC/120v power, depending on the unit, it will either convert the power to 12v to operate, or it will have a 120v element installed that will do the job, keeping the 12v element offline, to be used when desired when 120v is not available.....
in EVERY case, the control circuitry in the fridge needs 12v power to operate ANY time its turned on....
the ONLY reason to operated the fridge on 12v is for a brief period when you run out of propane.... otherwise, on 12v its just a waster of a precious commodity that can be hard to come by in some situations.... use the gas, or the 120v settings for the best performance...