My son is 11 but will be turning 12 June 9, 2013. The controlled hunt choices have to be put in by the end of May. He will have completed Hunters Ed, so can he put in on the controlled hunts this year.

He can get a hunting license as soon as he finishes hunter education (in this case, while he is still 11).  Be sure to get a junior hunting license, not the youth small game license.  You  can use this license number to enter him into a controlled hunt.  By the way--the application period is May 1-June 5.