The latest Blue Beret has an article on this subject. The article doesn't answer yes or no... but presents the issues for your consideration.
They express concern in the event of a traffic accident and spewing propane. (I discount that because the LP tanks have excess-flow protection built into the valves,...and if the tanks are damaged, whether or not the valves are open/clsd might not matter anyway.)
They also point out that refers can keep food cold for a day if the door is not opened.
An excellent point they make is that if the LP is simply turned off...but the appliance is NOT.... that the igniter circuit may repeatedly attempt to ignite (make sparks)...and that re-fueling fumes or an accident which creates a propane leak can then be ignited. Their advice is not to simply turn the propane off...but to also turn the appliances OFF.
I will continue to travel with propane on, and refer cooling on propane (although if I replace the refer at some point I will look into a
12V model also. I wonder if there's a
12v aftermarket modification available... Hmmmnn...)