An age-gap between two men is not as significant as between a man and a woman. And even those can sometimes work.
Should you do a man-thing with a boy at work? Meh. Not sure myself, mainly because of the work thing. I do know that as a boy I was very grateful to the men who acknowledged me as a sexual being. But I'm glad I met them outside of a work or educational situation But he's leaving soon for a bigger world, so I dunno.
Speaking as a 54 yr old who dated and jointly decided against a sexual relationship with a 21 yr old (the dating was at his instigation I hasten to add, my official age range is 40 - 60, he got under my radar because he's exceptionally mature and a good person), it sounds like you've got the foundation for a potentially good friendship anyway. Though it will involve some guidance and mentorhood. Are you ready for that? Do you have anything to contibute to his life? Or should you let him go and do his stuff? He sounds capable.