A 2,000 watt generator might or might not power the AC, it would be iffy, some would work, others not, and in any case you would not dare run anything else, even just the house battery charger built into the system.
In any case, running the hot water heater or the fridge on power from a generator is silly. Both run of propane, and would be much more efficient on propane anyway. The hot water heater, particularly so. On propane, it's probably at least 80% efficient. The engine in the generator is at best 33% efficient, throw in 90% efficient at the generator, line losses, and at best you are looking at overall about 20% efficiency.