Thoughts on applying to internships that I am not qualified for?

Hi all,

First post here, I am currently a rising sophomore student at a semi-target school on the East Coast. I have already started networking for my summer 27' junior year internship at some EB's and BB's. 

The main question is that I spoke to an IB analyst at a BB (Think GS, JPM, MS), and they had mentioned that they actually did very little networking and blindly applied to Junior year summer internships when they were a freshman. It worked out somehow, as the person had gotten a summer analyst position at one of the BBs listed. I don't understand how, as they were Int'l and did not meet the graduation requirements. Is this something worth doing? I have stacked up quite the experience on my resume for a rising sophomore, and am currently a summer analyst at an international manufacturing firm within their accounting dept. 

Is this something I should shoot for? I don't see how it could hurt, I mean the worst thing would be a simple rejection, but best case, I somehow get an interview. I would probably target some MM firms, obviously, I would rigorously network with alumni beforehand for as much of a chance as possible.

Thoughts?