When I am obsessed to see how long I can get a propane tank to last, and that includes some long drives, I run the fridge on the batteries while driving. Short drives to the campground, it is running on propane. I have never thought about turning off the propane while filling up but, I am thinking now there are laws that I am breaking. Will fix that from now on. Every ferry I have been on has required me to turn the propane off. Something to research if you plan on being on a ferry for a long period of time.
I have ran the refrigerator on battery between home and the campground and have forgot to switch to propane when I arrived. No, the refrigerator does not switch automatically. I was lucky in that it was only about an hour before I remembered. But one of these days, I am going to get nailed. I just hope it is a sunny afternoon so my solar has a change to fix my mistake.
Steve