To answer your question: I did interview prep with some anaesthesia residents I know through "my fraternity." One of my interview panel members was a "fraternal brother." And I frequently see my "fraternal brothers" at work. Three of my closest friends were "fraternal brothers" and they are now surgeons who I hope to work with once I enter private practice. It has played some role in my professional life.
However, I'm not sure how things work in Amercia. in Australia it's very common for doctors to have been born, studied medicine, and then go on to work in the same city. Therefore networking during medical school is a fantastic opportunity. Medical schools have "pseudo-fraternities" or "secret" branches of their medical school societies that are involved in the more risque or controversial aspects of medical school life.
They are all-inclusive groups meant to support and nurture growth and friendship, but they do so in a fairly inappropriate fashion (alcohol). There is no bullying allowed, no "pledges," absolutely no drugs. The societies are a fairly accurate representation of the medical population as a whole in terms of minorities, sexual orientation, etc. It's just a bunch of guys (or the girl-only equivalents) that get together to play drinking games and then go into town after to meet up with their fraternity/sorority coupling.
I met my wife through our medical school's "fraternity/sorority" combo. And the "secret societies" made my years at medical school the greatest years of my life; all of my closest friends (including my wife) are from that time period. I just signed up so I had something to do on Friday nights and didn't believe it would ever lead to much or be something that I would come to seriously enjoy. By the time I finished medical school I had had enough of the excessive drinking and moved on, but the friends I made during those years still stuck.