About the only thing I run on the invertor would be the entertainment equipment.....anything else, like AC's, Microwave, I turn on the generator.
If the engine alternator keeps the batteries charged while driving, then I don't see a problem there. The only other problem, might be dry camping.........and if I had to run the generator in the morning for awhile and the evening for awhile, I don't see a problem, for the type of camping I do.......actually, I do very little dry camping........genertor is always there if I need it.