Obviously the blower and controller don’t consume anywhere near the amount of energy that gas delivers, but it consumes more than most people think. The blower on a typical furnace consumes 75-400W per hour of operation, depending on whether or not it’s a single speed or variable speed type.

400 watts per hour isn’t a huge amount of power, a space heater consumes about 1,300 watts per hour, but it’s still a pretty decent chunk of electricity. A deep discharge marine battery (common for cheap backup power) could keep a larger blower running for maybe 3 hours tops, assuming an unreasonable 100% discharge and 100% conversion efficiency. So, not a lot, but still something that you’d need some pretty specialized backup gear to run.