Welcome.
Actually modern electronics are designed to accept a lot of junk - including modified sine wave - by design. Very few things may have problems, usually things with built-in chargers like rechargable shavers and odd things like X10 controllers. Computers, modern televisions, etc, are all ok on modified sine wave since their internal power supplies convert it to DC anyway. Microwaves are a special case and operate more like motors in that they need to run about 30% longer to do the same heating on modified sine wave, but they do work.
The built-in chargers in generators are very poor chargers and won't keep your batteries topped off while running the A/C. They are barely trickle chargers. You would need to use a high-capacity charger operating from the 120 volt output from the generator. That said, a 1300 watt-hour load @ 120 volts equals well over 108 amp-hour at 12 volts and no charger can support that. You would need even more than 108 amps after the losses from converting from AC to DC then DC to AC, and taking into account starting surges over time. Most consumer chargers will only output 50 amp-hour max and then only do it for a short time to help start a car. They usually will only output 20 amp-hour continuous.
Motors use up to 30% more energy while running from modified sine wave. My A/C uses about 1000 watt-hour with the internal fan on low (on pure sine wave), which would be about 1300 watt-hour on modified sine wave (this is the figure I used in the last paragraph).
As you increase your battery's output voltage by hooking them up in series, amperage stays the same. So you have 220 amps (not amp-hour) @ 12 volts. If you had hooked them up in parallel you would have 440 amps @ 6 volts. Either way your total power is the same, amps times volts which in both cases is 2640 watts. However, most of the time lead acid batteries should not be taken below 50% state of discharge so that leaves you with 110 amps available - or about 1320 watts IF you discharge them at a 20-hour rate (about 65 watts per hour for 20 hours). The quicker you discharge a lead acid battery the fewer total amps are available. Look up Peukert Effect for details on that.
So bottom line, it isn't going to work. I see where you were going with the idea but there are a lot of details which won't make it feasible.
I have considered installing a special type of A/C which uses a lot less energy (about 300 watt-hour) but even that would require six 110 amp 12 volt batteries to run it two nights for 8 hours each night. The standard RV A/C just can't be run from an inverter for very long unless you take thousands of pounds of batteries.
------------- Doug ~ '10 171 (2009-2015) ~ 2008 Salem ~ http://www.rpod-owners.com/forum_posts.asp?TID=1723 - Pod instruction manual
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