Switching Refigerator Modes?

I’m usually at campgrounds that have electrical hookups (at least), running the refrigerator on AC. When traveling I normally use DC. I may soon spend some time at a park without electric, so I plan on mostly using the propane option, which I haven’t previously needed (it works). However, the generator rules are pretty liberal, and if I need the air conditioner I’d be using the generator for a significant part of the day/evening. Is it worth it to switch the refrigerator to AC if the generator is in use, or do you lose cooling efficiency by stopping & starting so that it’s better to run on propane continuously? Want to keep my beverages cold!