I have used LP cooling and 120v cooling
An LP absorption fridge uses a small flame and less l.p. Than cooking or heating or the water heater, but it is still the same amount of energy btu's as produced by the electric heating element, energy use wise, RV absorption fridge can not compare to a compressor fridge that uses 1/3 the amount of energy for better cooling effectiveness , my previous RV had a 120v compressor fridge powered by inverter, and I was very happy with it
This RV has a side*side 2 door RV fridge and I only use the LP setting, I will switch to 120v only if I run out of LP because I wasn't paying attention to my use, at that point I use the inverter to maintain the fridge while I make an Emergency run to the LP fill location 7 Miles to the open all night truck stop, with lowest l.p. Price available in the area,
No absorption is not cost energy efficient when compared to compressor fridge operation costs
L.p. Is energy dense , creating electrical energy for RV fridge operational heat is not efficient,
Can it be made to work ? Yes in some cases
But not for every case