What a cute little story you've told. It sounds nice, but it just rings hollow with common experience. I consider myself a fairly social person, I went to one of the best Universities in the world. At least at this point, none of the people I still keep in touch with from my school (a fairly large group) would be helpful to my career in any way. I highly doubt they will be in the future. If, by some chance, in my 40s, a fellow alumni is helpful to my career by virtue of an arbitrary connection we have I would consider it remarkable, and a little bit of a personal failure.

I would never make a favorable business decision for the person sitting across the table from just because we happen to share an alma mater. If anything, I would be guarded against it being an issue.

I imagine the average person feels the same way that I do. I'm not saying there aren't politics as you make your way to a senior position, but don't count on any help to get there.