I have a fridge on AC, and it works very well. It's just like any other fridge, only smaller, even including a freezer that keeps ice frozen.
I do turn off the invertor when leaving the truck off for longer than 12 hrs, if not hooked to shore power, which means emptying the fridge. On several occasions, I've forgotton to turn on the battery charger when running the generator overnight, and the truck has always cranked, so the fridge doesn't deplete it - at least overnight.
I think it's a tremendous asset - fridge and microwave mean a much better diet than 'fast food'.
Inverters R Us is a great site for learning everything you need to know about invertors, and how to choose the right size and kind for your needs.