It depends on many things.
I tried to get a medical waiver from the National Guard for over 2 years. The paperwork got hung up for no reason in Kansas City.
I got tired of the runaround, and went to the Army recruiter. 3 weeks later I was heading off for training.
In the end, a waiver has nothing to do with the recruiter. It is the medical people and paper pushers higher up that actually approve it. 1-3 weeks is the norm though.