Reddit can be a wonderful thing. The College Football thread portion of Reddit posted the number of NFL players, both draft picks and undrafted free agents who signed with a team, by school. The list encompasses the 2013 through 2017 NFL Draft (or 2012-2016 NCAA seasons).
It should come as no surprise that Alabama has surpassed everyone with 65 players since 2013. LSU and Florida are close behind with 61 and 60. With 51 players, the Clemson Tigers are tied with their Auburn brethren and the Oklahoma Sooners. As you continue down the list, you continue to find college blue bloods: Michigan, Miami, Southern California, Georgia, and Notre Dame.