Softball Dropped Third Strike Definition

Question
Because of the recent changes to 10U play and now having dropped third, we
had some umps come out to speak with our coaches. They left more confused
than before. I've been reading up on the dropped third ever since. I now
understand that it's really more a "non-caught" third strike, and know when
the rule is in effect. The only confusion I have ultimately comes down to what
a "strike" is. Of course, if it's a called strike, that's easy. Apparently if it's a
ball just out of the strike zone and the batter swings, it's a "strike." I've seen
answers up here where a ball is WAY out of the strike zone, and a batter
swings and that makes dropped third go into effect. so... if you have a kid
who's really not a pitcher on the rubber and she somehow gets two strikes on
a batter, and then rolls one 10 feet wide of the plate, can the batter swing and
then take off to an un-occupied First?

Answer
I would have to say yes.  I looked at the USSSA rule book before answering this.  It seems that this would work even though it is not how the game should be played.   I have never been around 10U sanctioned ball in my neck of the woods.  Our rec league at that age doesn't allow stealing  or advancing on dropped third strikes.  I could see some umpires calling the girl out pretty quickly for leaving the base early, especially if it was obvious that she was coached to do this.