Interesting concept, but there's no real explanation as to how Harry was the proper head to all those families. I highly doubt that probability.
Author's response
No, there really wasn't that much explanation made. There was some - mention of the stolen heirships, but nothing too detailed.
But of course, the probability is against it. Way, way against it. Then again, care to do the calculations that quantum mechanics would require to give the probability that someone could wave a stick with a feather from a mythical animal and have a feather float in the air? Harry's always been an odd-events attractor.
When I get around to expanding this, I'll probably expand on the explanation somewhat, but not too much. It's magic - and it's Harry - the rules are kinda weak to be binding The Boy Who Lived. Note, too, that Harry glowed as he left the room - and that I left that unexplained. It was fun!