So this is a per-room/per appliance battery system? Not sure how this would work for my oil burning boiler, which requires power but has no "plug". Maybe this is better for households that run 100% electric for HVAC?
The bigger issue is how many amps the heating system draws. Assuming it's really a furnace that pumps hot water, (as opposed to a boiler that sends steam to radiators) those pumps really do draw a lot of current.