Hey,
So I thought I'd throw my 2 cents in on this one.
I was fortunate enough to go to undergrad at a school which had a student run campus EMS system and it had a huge impact on my decision to apply to medical school. You'll learn a lot about basic medicine which will help you later on, and the experience itself (if it was insightful and a reason for you to apply to med school) will definitely help you out come interview time.
However, I preface this with a caution: Don't do this as a means to an end. Do it because you want to and because you are getting something out of it, do it because it is adding something to your education that you will look back on favorably.
I'm not sure exactly what you're current situation is right now academic wise, but if you are at a school which does not have an EMS system right now, you could look into starting one yourself. There is an organization that would love to help you (and any others reading this who are interested) in starting a campus EMS system at an undergraduate institution,
http://www.ncemsf.org/
Any other questions about EMS or whatev feel free to PM me, I did a total of 3 years of volunteer EMS service and will be going to medical school in the fall.