I don't think it's going to happen.
Going off of VGC numbers (not official, I know) and assuming the Xbox continues to sell at the same pace it has for 2015 up until now (just over 87K units a week) that would put the Xbox One at 13.821 million by the end of September.
That would mean the PS4 would need to be at 27.642 million by the end of September. This just won't happen. Even if the PS4 sells at the same rate it did for the beginning of this year it would land at 25.63 million by the end of September. That might even be too high because it doesn't have any big console pushing games (like Bloodborne) from now till the end of September.
Though realistically I'm not sure the summer will bring the kind of sales that we've seen up until this point in the year.
My prediction,
Xbox One: 13.25m
PS4: 24.6m
Bet with Adamblaziken:
I bet that on launch the Nintendo Switch will have no built in in-game voice chat. He bets that it will. The winner gets six months of avatar control over the other user.