I kind of don't understand your situation. An RV air conditioner should work in any type of room or building. The air conditioner has an air intake from inside and then it circulates the air inside the conditioner, passes though the condensing coils, and spits cold air out the other side. I don't see where having any kind of exhaust fan in the building, on the opposite side of the building would make any difference. The air conditioner is designed to run and cool in any enclosed space.
Now, in order to circulate the air in the building (or completely sealed up camper), a circulating fan would help... you know, a simple floor or desk fan to push the air to the other side of the room or down a hall or something. Thus ... some manufacturers use duct work in the roof of RV's for the cold air to make a passage to each end of the camper. But a center blast air conditioner will simply blast the air straight down. You may want a separate fan to circulate the cold air in the room.
But needing an exhaust in the building is not needed at all.
The only thing you'll want to watch for, is to make sure the air conditioner can sit somewhat flat and somewhat level. I've seen RV air conditioners on 5ers where they are located on the roof between the low spot and the high spot on the over hang, at an angle. It looks weird, but I suppose they work OK. Still, if I were doing this, I'd want it as level as possible.
Other than circulation in a room, an RV air conditioner works pretty much like a house window air conditioner. Hot air in, cold air out. Do you need an exhaust to run a window air conditioner?
Edit?
I re-read your post. Are you saying the trailer air conditioner is located between the roof of your trailer and an add-on roof above the trailer? So if running, the air conditioner now way to cool the air conditioner components themselves, thus building up heat and eventually burning something out ... no surround air circulation? If so, then yes, run the exhaust fan. I think I get it.
