In general no, alums cannot, but there are certain circumstances where they can.
1. The alum signs up as a volunteer assistant coach. Unfortunately, the NCAA limits the number of assistant coaches a team can have.
2. Qualify as an "Elite Athlete". There is a NCAA bylaw that allows alumni who are fast enough to continue training with the college team. I had a teammate that used his Power Bar sponsorship and his USATF qualifying time to qualify under this way. Essentially Torres, Cragg etc. would all qualify.
Those are the two ways that I know of that are officially legal. There is probably at least one more way.
3. Your schools compliance officer is not a total bitch, who hates your team. Because really, if your coach is ok with it, is it really hurting anyone to if there is one more person going on a distance run (which is probably off school property), or running around the track?