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Yes, you can and nothing wrong with doing that. Although there are some who will argue the point. Functionally, (as stated above), the refrigerator works best when in movement.

From a different perspective, the long-debated-argument is... should RVers travel with their propane tanks turn on and should appliances be running on propane while in travel.

Lots of arguments and even "fights" on these forums about leaving the refrigerator running on propane while fueling at gas stations. There are those who insist on turning everything off when fueling, there are those who say they don't. There's the argument, that the trailer is 20 feet behind the tow vehicle and far enough away from the gas pump it doesn't matter, and then there is always the ONLY one that actually occurred when someone driving a motor home fill with gas and spilled the handle on the gas pump across the refrigerator vent and it caught fire. (DUH!)

But, we always have the refrigerator on propane when traveling. Won't do it any other way, and so far, I've not blown up any gas stations in 30 years of RV ownership.

I always run the refrigerator on propane while traveling. Never had a problem.

Of course it is, everyone (most everyone that is does it). The only time you want to shut it down is when fueling your truck and then only when fueling, if the fridge is close to the fuel pump. Most people don't do that either thought they should.

Actually an ammonia fridge is most efficient when it's moving around. Helps with the internal flow of solution inside.