Hi Joe jmccen58,
Given your rig is a very large 31 footer, I would think the dash a/c alone would not be effective throughout the coach on hotter days, not so good a situation when people are in back while traveling. If that is your case, then you pretty much have to run the generator. At least you would also benefit from 110v operations.
Our shorter rig with less interior volume, lower ceiling, closer side walls, good insulation, thermal windows, and no slide outs, the dash a/c is very effective in back, as is the heater.
I don't have hard numbers, but running a 4000 Onan generator will use more fuel than the chassis a/c while driving . If parked and idling, running the generator versus idling the Ford-V10 chassis engine, I would think a 4000 Onan generator will be the more efficient choice.
Not everyone can ignore vacation costs. It's a good question to ask.