Nope. You will find that it is not economical to do so. 120VAC
refrigeration typically runs with a very high load while the
compressor is on. This might seem ok at first, since the
compressor is on for a shorter period of time, but as you increase the
power drain on a
battery, its C rating drops dramatically. For this reason, your 400 AH battery may only deliver, say... 100AH of useable
power when subjected to a massive draw such as a 120VAC
refrigeration compressor.
I have 120VAC refrigeration on my
boat, but I run it when the genset is on to freeze holding plates. No drain on the battery.
In my case, when attempting to run my 120VAC
refrigerator through my 1400 watt
inverter, I found that the starting capacitor on the 120VAC compressor is not fond of the type of electricity produced by the inverter. The compressor *almost* starts but doesn't. I tried this out to see if there was some kind of failover method I could use in case of genset failure. There isn't, in my case (break out canned and dry foods).
So the short answer is that it's not economical. A 12V system would be more appropriate to use during an extended
cruise if you are not running a large genset every day.