Depends how it is run/ organised.
Melbourne Uni has had continued success as most of it's players aren't uni students.
Some are often ex students, but it's generally just a normal organisation being run out of that venue. In the case of Melb Uni the committee is stable (non/ ex students) and the playing group has been pretty stable (again made up of non students and a few ex students). I was told last year there were no actual current uni students playing, and they obviously had an older more experienced, and pretty solid squad (Norton, Masunda).
The University it self would pretty much be considered a sponsor which supports the club financially, as they do across a lot of elite sports (amateur footy, hockey, soccer, cricket etc)