Yes they have a club team. As has been mentioned, many would probably mistake the varsity team for the club team but they are in fact, two different teams.
As bad as the UConn varsity team is, I played for one of the best high school hockey programs in this state and my former teammate, who is second all time on our high school's career scoring list was cut from the UConn varsity team trying to "walk-on" (which I guess everyone is walking on technically since there are no schollies, but he wasn't recruited). So as bad as the current UConn players are, they're still really, really good players and if this upgrade goes through, they'll only be that much better. UConn alums will soon pop up all around the NHL!