Runner Scores on Dropped Third Strike?

 
With a runner on third base (R3) and the batter (B1) with a 2-2 count, the next pitch is a curve ball that bounces on the plate. B1 swings and misses but the pitch gets past the catcher. The catcher retrieves the ball and swipes at R3 (who was attempting to advance to home on the dropped third strike).
 
R3 is safe on a close play at home, but the catcher then sees that B1 has not advanced very far toward first base on the dropped third strike, so the catcher throws to first base to retire B1.
 
Does R3's run count?
 
Call
A run is not scored if a runner advances to home during a play in which the third out is made by the batter-runner before he touches first base (NF 9-1-1a). In the situation below, although there was another play prior to the batter-runner being retired at first base, the run still does not count (NF Casebook 9.1.1F).