I can't imagine anyone really would...but you wouldn't want to use everyone's misc. GPS - half of them have corroded contacts and all sorts of issues making connectivity impossible.

To do this (and I think it's a neat idea), the race (or whoever) would need to manage a specific gps, take care of mounting it, take care of retrieving it, and take care of uploading the data. Otherwise it just becomes really cumbersome on part of whoever is trying to make it all work.