Sometimes, but it is a harder problem than powering a gas-furnace blower. A heat pump is a 240-volt compressor with a starting surge, and in cold weather it may call electric resistance backup — a large, often sudden load. Honda’s home table does not list central heat pumps, so this site will not invent running or starting watts. Use the outdoor unit’s nameplate and the backup-heat nameplate, and assume the backup heat might start during an outage unless the installer can lock it out.
This question is becoming common as furnaces are replaced. The honest first split is: are you trying to run the heat pump as your only heat in a winter outage, or just to keep a freezer and a few lights on? If it is the first, you may be in standby-generator territory, or you may need a dual-fuel system whose gas furnace can run on a much smaller generator (blower plus controls only).
Enter the nameplates as custom 240 V loads in the calculator, and talk to both the electrician and the HVAC contractor before you promise anyone that “the portable will run the new heat pump.”
This is not a permit calculation, a utility approval, or a substitute for a licensed electrician, HVAC contractor, or the authority having jurisdiction. Panel Headroom is an independent educational site. It is not a utility, a certification body, or a contractor. Electrical and generator work that is done incorrectly can cause fire, shock, or carbon monoxide poisoning. Use the adopted electrical code and manufacturer instructions; pull permits where required.