From other postings I've seen where people have tested running their A/C off batteries and they are reporting that you can get about 1 hr of run time for each 200aH of battery.
I wonder how long it will be before RV manufacturers start offering an option of placing Lithium-Ion (or sodium) batteries in the generator bay, installing an inverter at least 2800W, wiring all the 110v outlets and appliances in the RV thru the inverter, and putting Soft Starts in the A/C. And with Lithium or sodium batteries, installing the second high-output alternator in the chassis in addition to as much solar as then can fit on the roof.
While recently researching for my next RV I found one that I liked which I thought could be built this way quite easily to match my camping style. (I'm not looking to run the A/C on batteries other then when I'm traveling, hence the second alternator. Plus future battery technology may improve well beyond where it is now.) I figured I could replace the generator with about 1200aH of Lithium batteries (pricey, but doable). When I contacted the manufacturer with my requested changes, they flatly refused - said the generator couldn't be eliminated and they'd never wire the A/C and microwave thru the inverter. Reluctantly crossed them off my list and moved to other manufacturers.