Sure that could get you somewhere! Particularly if you are motivated. I was in a similar position as you. I was actually in my third year of a bio-chem degree when I switched to computer science and engineering. I though tI wanted to be in health care...but all of my electives were in CS. Computers were a mojor hobby. then a professor said "you know you can make money doing this". for some reason it never clicked, you can make money doing something you enjoy!
Anyway, long story short, I would add a couple electives in development and programming. this way you get to see that world too. it looks like it is primarily networking. The biggest advice I could give is, be curious...then be curious about being curious...then learn and learn. Just latch on to what ever amuses you and be creative. the beuty of this field is (for now at least) is that you dont really have to have a specific major to do a specific job. Get the degree and get as smart as you can on what you enjoy. Before you know it the good life will come. I have this idea that if you get paid for something you would do for free or a hobby, you are rich.
CISSP, C|HFI, Security+, Network+, XYZ...blah.