not going to happen (running A/C off an inverter).
window A/C will cost you more in the short term - here's why:
Your 7 amp at 115VAC equates to approx 70 amps at 12VDC (obviously ten times the current). Startup will require higher current
. That equates to a minimum of 800W but with power factor and inefficiencies, closer to 1000W so it's not the inverter which is the limiting factor but your battery bank.
Put another way, to run your A/C for 5 hours will require a battery bank of approx. 800 a/h MINIMUM.
You'd be spending more on batteries than the proper marine