Just for laughs I tried my "new to me" 1981 Dometic electric/gas fridge (maybe 3.5 cu ft? not big) on "electric" 120v (not the 12v option it has) in the truck camper we got.
On inverter it draws 10amps DC on electric. I do not know its "duty cycle" I looked at various small fridges at the 3.6 cu ft size and they claim to want about 1a AC (it varies up and down by brand etc) so that checks out using the 10 to 1 rule for 120v vs DC via inverter.
So if left on inverter that 10a draw is 120AH for 12 hours if the duty cycle is half and half. I think from our actual RV fridge in the 5er the duty cycle would be more like 75% in the summer, so for 24hrs that would be 180AH to run the teeny weeny 3.6 cu ft fridge!
It starts to add up! So in our case I think we will run the fridge on gas for a long weekend. A full sized Residential fridge would be quite a challenge, but could still be worth it off grid if you do like Mr Wiz and run the gen for a bit in the morning and have lots of solar to finish up before dark.