If the power is out and you're running a generator, I don't think the neighbors really have much of a leg to stand on for noise complaints. New models aren't very loud at all and you could always put it in a big rubbermaid to help reduce the noise.
BUT, if a generator isn't your route, a battery backup will be fine. I'd recommend a big UPS that is designed to keep a small office running (they're usually like $150) as opposed to one that just runs a relatively low watt computer.
Yes, a heater uses a lot of amps. A small hydor pump runs at 10 watts, which is only .09 amps at normal household voltage. A small 150 watt heater, on the other hand, uses 1.3 amps, so it's draining 14 times as fast! (more or less)