If you have to leave a plane because you cannot occupy your seat, that's (by definition) an IDB.
Sure, but that's subjective. Just because you say you can't occupy your seat because of a POS doesn't mean that the airline will agree. I'm just saying you're going to have some negotiating to do before the lead GA sends a plane out with 1 empty seat while at the same time writing you a $400 check and giving you a seat on the next flight.
My sense is that she'd (a) try to reseat people, even if it means putting you in a middle seat somewhere, (b) offer to confirm you a seat on a later flight, waiving the change fee as a courtesy, or (c) tell you to get back onboard and fasten your seat belt before you're thrown in the standby pool for the rest of the day.