Yes, it will actually work. I know it’s very much not to code, but when we lost power for over 10 days, I did this to keep our furnace running and us from freezing to death since it was -10F out.

I only have a small 120V generator, but hooked both legs to hot and backfed via our EV charger’s outlet, since its a 50A circuit. Like you said, nothing 240V worked, but that little 3kW generator did a great job powering basically the whole house with no issues.

That winter was definitely a big driver for me to get a backup battery system so our solar could power the house.