support guys would most likely rush you a pair of wheels and its pretty obvious which wheel you need swapped. In most short races though, I see no reason to have spares. If you flat, you are done, nearly impossible to catch back up. Its different for crits though, since you have the free lap.

My team held a race a month back and one guy had a spare tire that was flat. Would have sucked if he flatted to find out that his spare was also flat.