Maine Sail, that APU system was designed for doing this day in and day out, most folks have 7 batteries in order to get about 7 to 8 hours a night air conditioning, I added three more to my system to get roughly 10 hours a night! It works rather well, when you have the right inverter! I had one that wasn't pure sine wave, I am getting ready to get a Xantrex 2.0 that should make it more efficient! One of the fleets in my area have been using the Dometic APU's for several years, they run several hundred trucks with very few problem!
It also has a shore power plug that will fully charge the batteries when I'm home on the weekends! The shore power will also run the unit! Several truck stops and more and more rest areas are equipped with electricity to make that easier!