Worst case scenario, they ignore your application and you re-apply close to graduation.
Best case scenario, they offer you some freelancing or part-time work and you graduate with some real experience and, potentially, a guaranteed full-time job.
Another good way to meet startups is to attend tech events. Go onto meetup.com and search for tech meetups in whatever area you're interested in. Consider favouring topics like Clojure programming seminars over things like "networking and margaritas for SEO rockstars" or whatever. The crowd will be smaller and more personal (and, in my contrived example, probably more technical!) and you will have a better chance of getting recognised as a regular participant in a small community. You get bonus points if you also volunteer to present an interesting project or something.