[diamond6]

Your scenario wouldn't work for two reasons. One, I believe the clock starts when the ball is kicked. Therefore, there would be no other plays. Two, there's no way the Patriots would have kicked straight away. They would have either squibbed it or short kicked it in the middle of the receiving team.

[diamond6]

Also, a squib quick is used precisely because it runs time off the clock. You can't fair catch a squib quick; it's fair game for either the receiving team or the defensive team to pick up - it's a live ball, as if it were a fumble.