If the setup is like it is on my motorhome, the generator (which needs 12V power to operate) is connected to the house batteries more or less directly--as starting it takes a lot of current--while often the converter connection is on the other side of the disconnect switch. If the generator is running and the battery disconnect switch gets activated, the generator will discharge the batteries and nothing will recharge them.
(Actually on my unit the converter is also connected on the battery side of the disconnect, meaning with the generator running and the batteries disconnected they would still be charged but there would be no power for lights etc. in the RV. I suspect that's not especially common, and more to the point doesn't appear to be the case for you.)
