Yes, I know what you mean, Stan. You are trying to maintain power during the switchover so the pot's circuitry doesn't reset.
But I often turn my pot on with no water added to its tank to reheat coffee if the automatic warmer gets shut off too early. It soon figures out there's no water and goes to warm mode. So I would either not fret about it, make the coffee with the inverter in the first place, or take Ed's advice re. a thermos, although I've never known one that kept things hot all that long unless full the entire time, and that wouldn't happen if you pour cups regularly.
To the base of the issue, I'm not really sure if having the inverter switched on with the genset running is doable or not. I'd have to give that some extensive thought, but would guess the inverter wouldn't actually start except after it sensed the lack of other AC, so there'd be a delay regardless. Our more electrically-inclined guys probably know for sure.
When I get up on boondock mornings I run the genset for a couple hours to get the Magnum panel to read "Float" or at least well into "Absorb" to cover the day to come. Thereafter we may use the thermos method and/or we do the invert just briefly as needed to microwave-reheat cups thereafter.
Joel