If your refrigerator is a dual voltage, AC/DC unit you might check into running
it directly off of DC rather than inverting DC to AC. (Most of these dual
voltage units only run on DC anyway........there's a transformer that converts
either 12 V DC or
120 V AC to 9V DC).

And your are correct. The limitation will be the size of the battery bank.
Three times the amp hours the application requires is a good guideline. Double
because you want to avoid discharging most batteries beyond
50% and the rest because you will recover
the capacity between 50 and about 80 percent pretty quickly but getting all the
way up to a full charge might take more charging time than you have available.

We run a small color TV/VCR off a square wave inverter, without any significant
problems. More sensitive electronics will appreciate a sine wave.