I was in the Sport Admin program at Belmont, so knew 6-8 people who had internships. I guess one or two of them worked for the Preds on a full-time basis after their internships. I also played hockey with some guys that worked there. I worked in ticketing, so I knew a lot of the ticketing staff as well.
Getting in with just a basic degree would be pretty tough. The best way, imo, is having contacts within the organization already. The sports business is probably the premier "good ol' boy" network.
My Sport Admin degree probably didn't help me learn that much, from an education standpoint, but was well worth it's weight when it comes to connections and opportunities. My advice is that if you are considering a career in sports, try an internship or job somewhere in the industry first, to make sure you like it, before you get an entire degree in it.