Thanks for all your comments and advice. As was stated, we will have to run the genie a little in October and April when it is a little warm which will help charge the batteries a little during the day.
My thinking is that if I can limit the amount of time I don't have to run the generator, I will save money on fuel ( off set the cost of the solar ) and wear and tear on the generator. I'm not sure what the hours would be, but I'm sure the amount of hours needed to charge the batteries combined with a little AC usage for each trip would add up to a lot of generator hours over the years.
Interestingly enough, even though our coach is 11 years old, the generator only has about 275 hours on it.