My furnace is a steam radiator system so it only needs juice to run the thermostat, open the flu and make the pezo-electric spark to ignite the gas. So it is a very light load. The battery/inverter setup can provide juice to the furnace/thermostat system for a long time. If the batteries get down, I'll know it and can recharge them easily. A small weed whacker motor that drives an alternator. 20 minutes usually does it. Uses very little fuel for that amount of time.
The major issue is it is not very stealthy. I'm working on that for the inevitable SHTF scenario.
I have a Nat. Gas Forced air system where I’d need to turn the blower motors (one motor for internal forced convection and one to provide outside combustion air and exhaust of same and the controls.