That size is usually big enough to run a blower and control board (and maybe a few other circuits), but it wouldn't come close to powering an electric heating element. But having a gas heater makes it all doable.
That's what we do, anyway.
Besides, at some point, you're just reinvinting an overly complicated combustion heater.
Which I already have, is already hardwired for fuel, and only needs to be plugged in.
That doesn't make the idea bad though. There have been attempts to do this in commercial furnaces before, but the details are hard, and ultimately of questionable value in general. In this particular situation it might be useful, but that is a lot of complexity for something that only makes sense for a week every 10 years.
Plus having a continuous plug-in (natural gas) fuel source is a big advantage over refilling a gasoline generator, which most portable generators are.