You'll have to check the power requirements for the A/C unit KP. Some are strictly AC and some are AC & DC powered. I don't think you'd get much runtime with an AC unit on just batteries. In that case you'll have to run the genny while underway. Most people I know don't do that, they open all the hatches etc. and get the breezes going and reserve the AC for alongside with shorepower.
Yours Aye! Rick
"It's not the boat "you built" until you've sworn at it, bled on it, sweated over it, cried beside it and then threatened to haul the POS outside and burn it!"