well, hold on now. If you increase the number of batteries you use, or convert to four 6v batteries and use a large enough inverter, say 3000 Watts you just might be able to run an A/C, but who knows for how long. Then you'd need quite a few solar panels to help keep the batteries charged.
It's about how much you want to spend and how long you will be able to keep things charged. I don't do this but know that a few friends have some very serious electrical supply systems to be "off-the-grid".
I would not read dieselguy's "no" as a "no way at all". He did qualify it that you would need some setup, and knowing how the batteries drain, how fast they drain with an A/C and what else would affect the drain and how to lessen the draw with a real good recharging system, it's not a resounding "no" but would probably be more expensive than buying and wiring a suitable generator. But not using a generator means you might save some weight (except with the better than average batteries that will be heavy) and not having to spend on fuel to run it. Then there's the noise factor, too.
The point being a solar system is lighter, quieter, does not need fuel but does require sunlight, so for extended storms a generator as a backup provides the best for all conditions if you are willing to spend on having all bases covered.
At my house I now have a Solar system and so far it is saving me a ton of electricity costs during the day. The only costs are because at night I am back on the grid so it will be a little while before I get the price of the system back (I do not have battery storage, yet). Same thing with an RV if you install the right stuff, except the batteries allow you to remain off the grid even at night.