Yes, I run my fridge on AC with an inverter while on the road. But, it's not because of any fear of propane leaks fire, or explosion. I simply got tired of trying to fix whatever was causing the flame to get blown out on the road. I had to significantly increase the size of the 12v charge wires to the camper battery so the alternator could keep up with the ~345 watt draw from the inverter though. Six gauge wires from the alternator to the 7-pin plug in the bed. You might have to go even bigger on a TT due to the length involved.
Those of you who advocate turning the fridge off should really think about what could happen if the wrong person blindly followed your advice. We don't all have the same fridge, we're not all from the same parts of the country, our immune systems aren't all alike, and we don't all load our fridge up the same way. I would recommend anyone considering this put a wireless thermometer in your fridge to monitor how warm it gets while it's turned off. Food safety is serious business, and keeping food at safe temperatures is key to keeping it safe. Every person who works in the food industry knows that you either keep it hot, keep it cold, or you don't keep it. The danger zone in the reefer section BEGINS at 45, and the higher it goes from there, the faster food spoilage occurs. That slightly tainted piece of meat or carton of milk that tastes a little funny might be tolerated by a healthy adult, but it could actually kill a child or any person with a weakened immune system.
Because I monitor the temperature in my fridge while on the road, I can tell you for a fact that the 12v mode on mine is useless. It won't even keep up with a moderately warm day here in the south (85 deg). It's a waste of amp-hours from the camper battery to try to keep it cold on 12v, so I unplugged the 12v element years ago. I can also tell you for a fact that the fridge warms up to above 50 degrees very quickly on one of the all-to-typical 90+ degree days we have around here. So as far as I'm concerned, it's either run it on LP (which isn't reliable on the road), run it on AC mode through the inverter (which works very well), or if both of those failed go buy a chunk of dry ice. Turning it off means food I would be hesitant to eat, and I damn sure wouldn't serve it to a guest.
:):)