Many, many security companies don't care what your formal education is. The reason for this is simple: there aren't many (or, perhaps, any) undergraduate computer security programs that are cutting-edge and relevant enough to teach the skills needed to be a good hacker. Unless we're talking about graduate-degrees, I barely glance at a prospective hire's formal education -- there's just not enough correlation between that piece of paper and performance on the job.
What I do look for is self-motivation, passion, and drive. I know it's cliché, but you can't be great at infosec if you're just pulling the 9-5 -- it has to be something you really care about. You have to stay on top of everything.
So how does one measure passion?
Clearly, if you can talk about side-projects you've done in the security realm, that's a great start. If not, being involved with the community (such as the free and local Security BSides conferences, OWASP meetups, etc.), shows that security is something that you really care about. Those events are free (or maybe $10), and show a lot of drive.
I know your actual question was in terms of IT disciplines, not just security, but I'm confident that what I'm saying here applies to almost every selective career type. You're trying to be competitive in a tough environment, so you have to make yourself stand out. Really, really wanting something usually shows.
That said, feel free to shoot me an email if you're still interested in the security route. I'm always looking for new engineers!