You need to at least double the running amps to allow for the surge the compressor needs every time it starts up. the motors that power compressors in refrigerators, freezers and air conditioners always take double or more surge amps. And you need the batteries to handle the power. But do you really NEED the inverter?
I have a 3 cf dorm fridge AND a 4 cf under counter freezer in our Class C. We have been fulltiming with this set up since Fall 2006. We have bounced these particular units from SW NC to S Ga, to N FL back to S GA, to SE TN, back to S GA, to N FL, back to S GA, to SW NC, to NE TN, back to SW NC, to Central NM, to S TX, back to Central NM. I think I missed a trip in there some place... When we came out west (the SW NC to Central NM trip) I ran the generator because we had worked an event a few days prior to leaving and we had a freezer full of hot dogs, sausages, etc. OTHER THAN THAT, we leave out with a fully chilled refrigerator and freezer unit. We do not open the door. We can travel up to 8 hours without the temps dropping. We pull in and either plug into a power pole at a campground OR run the generator for a few hours in the evening (watch a movie when wallydocking). Most refrigerators (even dorm type) can hold temps for up to 8 hours if you stay out of the units. My 2.5KW POS Onan has a hard time handling the surge with the compressors from the A/C unit, the refrigerator AND the freezer all kick on at at the same time. Which they cycle thru roughly every 1.5 to 2 hours or so. Run the generator for two or three hours and the units compressor will cool them back down. I do not make my units any colder than normal before traveling. We normally travel in one day trips but out west everything is farther away. So out here we make multi day trips. And we stay in parking lots at least one night, sometimes two.