Yes, but not in the way you are thinking. From 1921 to 1936, the University of Peabody was a semi-professional football team based in Peabody.

It started as an outlet for, post-high school and in some cases former collegiate, athletes to continue playing at a competitive level. The University of Peabody had no campus, no buildings, no students, just high performing athletes.

University of Peabody Team, 1921
Nathan F. Masterson, Senior, is in the front row, second from right. Top row includes Edward Brawley, Senior, who was a coach and teacher at Peabody High School from 1922 to 1926; he coached the University of Peabody team from the early 1920s to the early 1930s. 
The Boston Globe, October 18, 1929
The Boston Globe, November 29, 1926