I would submit your application asap. Some schools have already started inviting. If you have 3 other letters I would send those, use this as your fourth which you can go ahead and send to the schools as well. That way if he takes longer than a week it wont delay you. Basically send all 4 you have (if you have 4). When his gets uploaded it will automatically send to schools. You CAN get interviews without that 4th letter so waiting until it comes in is not worth it. Schools consider your app complete with 3.
Hope this helps
