Yes, the AC runs off the generator, just barely. I have to choose either the battery charger, or the microwave, or the AC, never more than one, and never the toaster oven, which takes too much juice unless I'm on shore power. The E2000 generator would undoubtedly handle more, but it doesn't fit behind the porta potti, and sticks out into the main cabin when stored, so I chose the E1000. It's also much lighter to lug around, and easier to carry aft outside the cabin to use.
The Wallas, when it works, really pumps out heat! In Carrabelle, Florida, when I was there in late January 2005 it got down into the 20's, and with the Wallas on its lowest setting, I still had to keep the door open. It wasn't very comfortable, with cold drafts from the door alternatiing with hot air from the stove. Later, in Atlantic City in May, a Nor-Easter blew through, with winds up to 40mph, and the temp down in the 40's. That's when the Wallas decided to quit on me, with smoke coming off the circuit board. It was cold and damp and miserable; probably the low point of my trip. Wish I'd had my little electric heater then! No stove at all for the last 1000 miles or so of my trip.
I didn't carry a Sunshower, relying on marinas or a swim. But as I said, I didn't anchor out much, because I didn't have the Honda generator then. I did have a 1000-watt inverter, and two type-27 deep-cycle batteries, in addition to the two starter batteries for my engines. Frankly, it wasn't just the lack of a generator that kept me in marinas most nights. I just felt safer. With a little more experience, now I enjoy anchoring out much more.
Regarding trying it without paper charts, my own preference would be not. I'll probably only do the one great loop in my life, so the extra safety offered with paper charts aboard was worth the cost for me. I was very cautious. I had two laptops on board, one as as a backup, and also a Garmin 2006C color plotter. I was never lost, nor did I ever run aground, and I attribute that to the extra care with charts and piloting. There are some places along the east coast where it's easy to make the wrong turn on the ICW. It looks like you're out in the middle of a big lake, but it's rocky and only a foot deep just a few feet outside the channel markers.