I purchased my student ADC membership on Tuesday night and faxed my ID, schedule, and passport Wednesday at noon (CST).
Later Wednesday, At 6:30 CST, I called ADC as I was not verified and briefly chatted with a very helpful woman. She went and checked the fax and verified me on the spot!
On Thrursday, I noticed that I did not have a hardware discount in my "Assets," so I called ADC once again and was told that sometimes it does not display for the student memberships, but I did, in fact, have a hardware discount active. So on Thursday I ordered my Macbook Pro!
In other words, you could probably buy your student ADC membership in the morning, fax your info, and be approved and using the discount by that night.