Yes, the refrigerator needs to be level or close to it. The reason is an absorption refrigerator relies on heat and convection to circulate the refrigerant. The burner boils the ammonia mixture, and the vapor rises to the top of the cooling coils. It then condenses back to liquid form and runs down a series of tubes to the bottom of the refrigerator, where the liquid is fed back into the boiler.
If the refrigerator is not level the boiler is no longer the lowest point in the circuit and it can run dry. If the boiler dries out it will cook the coolant, forming solid clumps that can clog and ruin the cooling system.
The refrigerator will withstand being slightly off level. But operating it significantly off level is inviting trouble.
It is OK to run the refrigerator while the motorhome is on the road - even though the refrigerator may not be level the motion keeps the coolant from pooling elsewhere so the boiler stays fed. But you should turn off the fridge if you stop for lunch with the motorhome significantly off level.
