My dealer recommended not having the refridgerator running (valve on propane tank open) while traveling. The concern he expressed was having an accident that resulted in losing the tank emitting propane at an accident scene. This is probably a low probability issue but never say never.
I was also under the impression that in some states running with propane on was illegal.
2012 KZ Spree Escape E204S
2007 Chevy Silverado 1500 4.8L, 3.23