The reason for keeping the fridge level is so that the liquid ammonia continues to flow freely via gravity and doesn't accumulate anywhere in the tubing while in operation. It also doesn't need to be exactly level, as long as it's close to level there shouldn't be any problem. So, unless you park it at an extreme angle you could leave the fridgerunning & it's probably OK.
When the fridge is off it really doesn't matter, just level it out before you start it up. If you have it at a pretty steep angle then it could take some time for the liquid ammonia to drain properly. So it could take longer to cool off when when you restart it. That might be why the dealer is telling you to keep it level when its off.
2011 Chevy Silverado Crew Cab 4X4
2009 210 WBS