The posts have been somewhat interesting and informative since I have no NCAA experience. I'm just reading out of curiosity. However, there seems to be some confusion about the OP's intention. Advice is being given about walking on, developing a relationship with the coach, making the team, etc. This guy has, and it seems, wants, nothing to do with his school's team. Or maybe you all are on the right track and becoming part of it IS, in fact, the end goal. It just seems to me from a literal reading of the first post that he's looking for competitive opportunities. Period. Not trying to figure out where and when his school's team is practicing and 'coincidentally' running by, trying to get their attention. You all are just suggesting slightly more subtle and slightly more complicated versions of that.
My advice is, contact the coach and see if the school allows it, but what I mean by 'the school' is the host of the meet and by 'the coach' I mean the meet director. I think that's exactly what several of you suggested, although the advice could be taken to mean: HIS school's coach, with whom he has and needs no relationship. Whether or not HIS school is tolerant of unattached running is irrelevant. All they affect is their home meet. The only people or organizations he needs to care about is whoever is holding an event he's interested in.
If what he's hoping to run is 5k or longer, road races are, in my mind, the best option. That's what I did in high school and it avoided a lot of problems associated with school teams. I certainly admire someone doing the same during traditional college ages, too. There's no tryout, no cuts, no roster, no politics, no rules (GPA, practice attendance), Coach doesn't like you, who cares. You don't ever even see him.