A couple of years back I had a vehicle fail with a few weeks left on the old ticket. Despite this, the car showed up as having an mot on the computerised system right up to the date the original expired.
So I would say the answer to your question is that you would still have a valid MOT, but you would be knowingly driving an unroadworthy vehicle.
1994 Frontera 2.0i Sport Convertable (gone but not forgotten)
2002 Frontera 2.2 RS dti Sport (current drive)