@Leehigh80
I don't know how long it would take for the therapy to work should they allow you to go through with it at OCS, but if you're not found qualified by graduation they may just redesignate you since at that time you would not be found to be physically qualified. It's all about timing. I'm not saying it will happen, just that it seems to work that way.
Guarantees don't generally fly in the military. Very few people can "guarantee" anything for you. It's the nature of the business.
Some food for thought though should you end up in API:
I can't speak to all the situations you mentioned but I do know that if you are found to be NPQ (Not Physically Qualified) for aviation in API, you will be allowed an opportunity to redesignate, you don't need to separate if you decide you want to stay in for whatever reason.
I have a friend who got NPQ'd and he's going up for a board to see if he can pick up Supply. I can't speak to your chances at getting whatever designator you want should you decide not to separate, since things change rather quickly, but that is an option for you as well. Just letting you know.
And we all know how the economy is these days.
As always, someone more experienced than I can will be able to give you more specific info on your issue.