score:6
TSA has size restrictors (the grey metal rectangle) in front of their hand baggage X-ray machines:
(Source: Wikimedia commons)
If your suitcase can fit through the size restrictor; then you could conceivably bring it all the way to the gate. TSA itself doesn't list any restriction on the size of hand luggage - they defer to airlines, however most checked suitcases are too wide for the hand luggage x-ray machine -- and if it doesn't fit, they won't let you fly (chances are that even if you raise a fuss about the lack of TSA requirements on size, they'll ask to see your boarding pass, note that your airline won't let it on anyway, and won't let it through).
Even if you get past the TSA, the boarding agent at the gate could look at the suitcase and deny boarding if they thought you were somehow gaming the system or would cause a delayed departure. Allowing gate checked luggage is at their discretion. More importantly, it takes time to tag and load gate-checked luggage and they may be under pressure to not let the plane departure be delayed.
So after all that trouble, the gate agent may put you on a later flight after all.