Does the run score?

[SAump]

BACKSWING HITS CATCHER - If a batter strikes at a ball and misses and swings so hard that he carries the bat all the way around and, in the umpire's judgment, unintentionally hits the catcher or the ball in back of him on the backswing (i.e. the followthrough), it shall be called a strike only (no interference). The ball will be dead, however, and no runner shall advance on the play. If this infraction should occur in a situation where the catcher's initial throw directly retires a runner despite the infraction, the play stands the same as if no violation had occurred. If this infraction should occur in a situation where the batter would normally become a runner because of a third strike not caught, the ball shall be dead and the batter declared out.

If it applies to strike one and two, it applies to strike three and to that "retired" batter.