NOBODY can predict that. Every situation and individual is different.
Is this his regular psychiatrist he's supposed to see tomorrow, or is this a new appointment he's supposedly made? I'm saying "supposedly" because it isn't unusual for alcoholics to lie about these things. IF it's a regular appointment with a psychiatrist he's been seeing, then it might be worth cluing the doctor in, explaining that he doesn't know about the planned intervention.
As for how long you might have to stay with your Aunt, same thing--no one here can predict.
I'd just suggest keeping your expectations for this VERY low.