One thing to be aware of is that many polys (though not all, by any means) consider don't ask don't tell (DADT) policies to be a red flag. It's easy for the person 'not telling' to actually be cheating with no such agreement, and the other partner has no way of confirming or denying that a DADT agreement is in place because he/she can't meet the 'not asking' partner.
That your friend-with-benefits seems reluctant to let you meet his girlfriend makes me concerned. What I'd recommend to him if I were in your shoes would be a large group outing-- all three of you, and a bunch of college friends: bowling, a diner, maybe just a movie or board game night at home. That way you can find some time to sit near her and chitchat, and she can get to know you as a person. Like Eugene said, it's much easier to swallow the idea of something when you can attach a face to the situation, and it could be that that's all she needs.
All that aside, I have a question for you. Is the relationship, as it currently exists, meeting your needs? Does it seem to be meeting the needs of the others involved? It might be that the current, ambiguous situation is viable, and that's a possibility that's at least worth contemplating a moment. Getting into polyamory for me has been about giving up the binaries and labels in thinking about people: gay/bi/straight, dating/friends, primary/secondary/tertiary. Relationship styles that are new (for me) are part of the fun.
Good luck, and thanks for sharing! Keep posting on here-- we're here for you.