Hey All,
Here's a brief snapshot of my experience with networking for consulting recruiting having gone through it successfully myself.
Networking at B-School is a bit different than networking in the "real world". The networking (company presentations, coffee chats, office visits, etc.) is really more a chance for you, the student, to get a sense of what each consulting firm is like. You take the time to speak with consultants at different firms so that you get a feel for who you'd like to work with and so that you understand what the differences (sometimes subtle) between the firms are. You can then use this information in your cover letters or during the fit portion of your interview to demonstrate your knowledge of and compatibility with said firm. I don't believe (just my opinion) that anyone actually separates themselves "from the pack" during networking and that you will do perfectly fine if you are professional, polite, and ask thoughtful questions about what it's like to work at XYZ firm. It's not a bad thing to develop close relationships with people because you'll get more information, but I don't think it's make or break.
As far as resumes, case prep, and interviews go, that's another explanation.
This is just my experience -- happy to hear about what other's went through. Hope this helps!