As an enlisted navy man myself, it would be a big surprise if Keating went to the Academy knowing his rank (Chief, which is E-7). SEALs do advance fairly quickly, so assuming he went to boot camp shortly after leaving IU in the spring semester of 2006, this would have been his rough timeline (note, I don't know his specific timeline, this is just an educated guess based on what I know of the SEALs as well as how navy enlisted promotions work. I am also making the assumption that he earned enough college credit to enter as an E-3 and skip a few of the early pay-grades).
August 2006: boot camp (~8 weeks)
October 2006: BUD/S (24 weeks)
April 2007: Jump School (3 weeks)
May 2007: SEAL Qualification Training (26 weeks)
November 2007: Assignment to SEAL team
May 2008: Promotion to E-4
December 2008: Promotion to E-5
December 2011: Promotion to E-6
August 2015: Promotion to E-7.
There is a chance that he promoted quicker based on his evaluations, but there is no chance that he actually went to the academy based on a few factors. Additionally there is now an 8 week BUD/S prep course that is after boot camp, but I do not believe that was around when Keating went thru.
1) He is enlisted, not an officer (which all academy grads are).
2) There is very little wiggle room in the promotion schedule I outlined for him to attend the academy and either fail out or drop.
3) I would be very surprised in the SEALs accepted an academy drop immediately.