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You need electricity for the blower motor to force the air through the ducts of your house

The original comment is comparing to radiator heat not forced air.

My boiler system has an electric pump. I'm not sure my boiler would run without electricity either.

~30% of the NYC area is still probably running steam heat which just uses physics to get where it's needed.

Depending on the system size a car battery and inverter can run a forced hot water system for a pretty long time.

Forced hot air is gonna be worse than that but the electricity to run the blower is still peanuts compared to a heat pump system.