DRat, yes, the furnace runs on 12V but if you are on generator power the demand on the batteries will work the charging system more thus demanding a bigger draw on the generator.
Everyone, on a side note but related, make sure your generators are not contractor grade but are inverter types or you could damage your sensitive electronics. Even if you maintain generators well there is always a risk of bad gas causing the engine to not run perfectly and then you'll get dirty power, which can and will, damage electronics. These electronics include your TV, computers, stereos, the circuit boards in your microwave and fridge, etc. Inverter types give clean power no matter what and will kick out completely if the power is not right. To save a couple hundred dollars on a generator I wouldn't take the risk with the contractor ones.