The problem that with using a generator to run an A/C is that they will not start. Some people have been able to get their A/Cto start with a Honda EU2000, but most have not.A few weeks back someone was asking about powering a 16kBTU Cruisair with a 2000 and despite the warning that the problem was not "run" but "start" he bought the 2000 anyway. Guess what, it wouldn't start. Motors can draw up to six times the run amperage on start . There's no way a 2000 can handle that load even a momentary load.
As far as charging batteries, the 1000 will run a 80 amp charger.
This is correct. I have a 12,000 BTU Mermaid Marine Air heat pump/AC unit, and I've already established that the start load is too much for an EU 2000, and probably also exceeds my already purchased 2000 W Xantrex inverter. The weight, space and cost penalty to "solve" this, while doable, is excessive, so we won't have A/C away from the dock. We'll have 12 VDC fans, windscoops, and for chilly nights, a diesel bulkhead heater. Even a couple of oil lamps and a deck hatch left open a crack to make a vent to encourage air circulation makes a difference.
Basically, A/C is a shoreside luxury, unless you are willing to get into built-in gensets and vast inverters. My idea is to have a bank of three or four AGM 8D batteries that I keep well-charged, plus a separate wet-cell start battery, and finally a separate wet-cell deep cycle for the windlass, which is also manually operated.
The EU2000 otherwise hits every sweet spot as a luggable genset (20 kilos) that doesn't take up much room. It will charge my banks, power my AC power tools around the boat, can be taken ashore easily and is the backup to my backup of wind, solar and alternator. It even has enough amps to run a radar set and an SSB if everything else is fried electrically. As I will be carrying 10 or so gallons of gas for a small outboard anyway, it's really no hardship.
If Honda made a diesel EU2000, even if it was ten pounds (25%) heavier, I would go for that in a flash.