Yes I have used my 300w GoPower inverter to power the Dometic absorption fridge. Pulls almost 30 amps from the 12v battery when the cooling unit is cycled on. Most batteries will be dead in a couple hours. Probably 400 to 600 watts is actually plenty as I believe the heating elements are about 325 watts.
I used mine when leaving town and the propane burner would not light. No time so used the inverter until I was at location and was able to get the propane going again. Turned out to be a loose connection to the propane valve solenoid.