I have to say that while I think it's possible, it wouldn't really fit. The whole point of the original is that Michael IS the bogeyman--there's no reason given for it. It's not that he was abused or neglected as a child, raised in a wildly dysfunctional family, or even was replaced by his new baby sister as his mom's favorite. He just IS evil. Zombie's film gave him too much of a backstory, which--at least to me, and I realize this is probably highly subjective--made the story less chilling.

You would also have the problem of Halloween II and the flashbacks there, if you wanted to involve it in the whole series.