Hi M&M and welcome to Greek Chat!
I do believe it is possible. Like sororities, fraternities allow alumni initiations on a case-by-case basis with certain standards according to their bylaws.
The very first time I learned about alumni initiation at all was when my husband was showing me his KA Order gruop photo. He had one of his professors in his pledge class, and he ultimately became a faculty/alumni advisor to that chapter.
Good luck!
Adrienne
