I saw a cord and plug connected furnace once.
It was a friends house and he called me because a furnace repairman was nearly electrocuted while working on it. He refused to come back until it was wired correctly.
Someone had come in a coupla years earlier and added the cord & plug so the furnace could easily be hooked up to a generator if power was lost.
Problem was now the 120v was coming down the nuetral side into the furnace then up to the switch. Tech didn't check for voltage after turning off the switch. I took out the cord and plug and gave the guy a small transfer switch that runs the important circuits.