I think it certainly wouldn't hurt (but then, I would say that, wouldn't I?)
Seriously though, since you're a student it's free to file your CV, and it's a great way to show that you're serious about your craft. So even if you have to send it along to employers when you're reaching out to them (rather than them finding you on careers) you'll still have a leg up on those that don't have a Stack Overflow CV.
In addition, you will show up in search results. Companies have been known to look for interns (no stats, sorry) and having a CV on Stack Overflow will tell them you're serious about getting a great job (or possibly a great internship for starters), and that you know what you're doing.
Finally, your CV will be marked as "student". If I had a company with an internship program and I would see a great student on SO Careers while doing another search, I'd file them away for future reference.