Propane..unlawful to have fridge on...is incorrect...

This doesn't just apply to this subject, but many others. If something is illegal, will your insurance company cover your losses.
This applies to propane, no-toad brakes, overweight vehicles & improper drivers licence. A conversation with your insurance company might not be a bad idea. I don't think a judge will take into consideration that a conversation on the internet is an excuse. YMMV.