^ The light switch for furnace power is typically installed near the ceiling, least around here, so it's pretty hard to accidentally flick it, I can't even reach mine without a step-stool. The furnace side of that switch wiring, once disconnected from the switch, is where I'd feed in the 110/120VAC power from the inverter or generator.
As far as the fan motor, it would suck a lot of power. That's why I wired mine so I could switch the fan right off, that is not the "normal" way to wire around here...normal here is so that the fan is always on, on "low speed" even when the thermo says it should be off. This was costing me too much, I estimated $25/month 20 years ago.
Also, I completely shut off the gas to my furnace during the warm season (saves about $60 a month from the stupid pilot and HIGH gas prices now), so I don't mind re-lighting it, it's not hard.
Are you getting the idea I'm a bit cheap here?

Oh well, now we can call it my stylish contribution to reduce global warming...