First, I don't think it would be a very safe idea. Secondly, I doubt it would stay lit. There is a sail switch that has to be made for the flame safequard to allow the burner to light and stay lit. Between the air turbulence on the inlet and exhaust of the combustion chamber changing the airflow through the burner, and the inertia from the road and suspension bouncing would keep it from staying lit for very long. Third, the furnace flame safeguard locks itself down on a failure, unlike the refrigerator. It has to be manually reset at the thermostat.
Lastly, your vehicle would maintain the 12V supply to your RV so, no you wouldn't need a generator running.