As someone who actually attended Columbia College and received a bachelors in Film Editing, I absolutely regret it. Given, I was technically proficient in editing and basic camera work prior to attending the college, I was sucked into the pressure of needing a degree to get any decent job. The opposite could not be more true. It's all recommendations, and your portfolio. Oh, and doing a lot of stuff for free the first time around so people will give you a chance.
Making connections was probably the best part of the college, but not worth $20k a year ($20k in loans now). You're better off doing what everyone else is suggesting, learn your craft, generally at first and then specializing when you find your niche and then just creating and creating. Learn from your mistakes and continuously improve and try new things. If you want to make connections with other film students and indie projects, make the commute to the film building every other week and check out the events posted all over the many bulletin boards.