dropped-3rd... does run count?

Question
12U ASA Softball.  We have a runner on 3rd base.  The batter swings at pitch which is the 3rd strike... catcher drops the ball.  

Runner on 3rd comes home and safely touches home plate before the throw from the catcher gets the runner out at first base.

Does the run count?

After a brief conference, the Blue Crew said the run counted (which is what I thought) but I wanted to be certain for future reference.

Answer
Hi James,

the answer is NO, the run dos not count. By rule anytime the b-r does not safely advance to 1st base  and it is the 3rd out of the inning no run can score.  This is basic umpiring and the PU should either know better and/or go to some umpiring clinics.

Mark