The original Dometic in my '67 Overlander (don't know the model) has a plate stating it requires 235 watts to run on AC.
So you could definitely run my refrigerator with your inverter. You are probably okay, but look around your unit & see if you can find a similar plate.
Your real problem will be feeding the inverter. Your charge line is probably only rated for 20 amps dc. 235 watts takes about 19-1/2 amps. Although your inverter is up to the challenge, your charge line may not be.