Someone please correct me if I'm wrong. When I think about how a school would track you down on a forum like SDN, there would be some huge roadblocks. First, they would have to get the site to comply with the request for your IP/MAC address or your social media information (if provided at sign up). Based on comments in this thread from mods, it looks pretty difficult. However I can imagine it'd be done with a court order. (So don't say anything that might land you in court?)
But let's say there is some way they can know who you are without going through the moderators because you posted a link to your Facebook and posted a lot of details about who you are and your current school. At this point, everyone and their dog knows who you are (and your life may be awkward at school now) but if a school wants to act on this information, the burden of proof is on the school. However unlikely it may seem to a casual observer, people have been known to change their identity on the internet and say they are doing things they are not. So unless you admit that the posts are yours I have a hard time making the leap between a school knowing who you are and actually throwing you out of a program based on that knowledge. What if your little brother is a troll and a premed, so he pretends to be you on the internet to gain more credibility on this forum? Same IP address, intimate knowledge that you may have shared with him and some offensive or unprofessional behavior. I think banning this IP address would be the most reasonable course of action but potentially throwing out an innocent student seems like an overkill unless they have really concrete proof.
However the golden rule still applies. Don't say or do anything you wouldn't say or do in front of the Dean and you'll be alright.