triple play and run scoring

Question
Baseball situation:
Bases loaded no outs.
Line drive to short stop, who steps on second and throws to first to complete the triple play.
The runner on 3rd runs for home on the crack of the bat (no tag up) and crosses home before the triple play is completed.
Does the run count?  
The run was counted because it was not appealed that the runner did not tag.  My thought was since the runner crossed home without legally retouching 3rd anyway, the offensive team would have to appeal that the run should count and not the defensive team appealing that the run did not count.

Answer
Kevin,

The ruling was correct.  The team must appeal to get the 'fourth' out so that out would take precedence over the third out that was actually made.  The proper appeal is to have the pitcher throw to third base before the team leaves the field.  As soon as they leave the field, the play stands.

Hope this helps!

Brian