If you want, I'll give you the long version of it, but bottom line is you'll have to start at the bottom (helpdesk) and work your way up. Because a sysadmin tends to work with very critical systems, you'll have to build a reputation of handling more and more responsibility with the same amount of precision. Basically, you'll need to outshine your peers for quite a while.
That being said, I've worked with both degreed and non-degreed people. Experience is the only thing that ever seperated them. Degreed people, I've noticed, tend to complete jobs more often; but I have found that they also tend to think a little too highly of themselves and ignore the people who have been doing it for years.
So, it'll be a struggle, but I, along with quite a few other /.'ers, are living proof that it can be done.