Depends on the course and the race. A good wheelset might weight a pound less than a training set, which will matter if it is hilly or if you are accelerating a lot (as in a crit). A good wheelset might be quite a bit more aerodynamic and might save you 5 or 10 watts at 25mph. Races are won by all sorts of time ranges, from minutes (hill finish), seconds (time trials), to milliseconds (sprints). Whether it is cost effective to have a fancy wheelset is totally up to you, your goals, and your resources.

All that said, having a second set of wheels, even if they don't fall in the "bling" category, the redundancy of a second wheelset and reliability of relatively unworn tires is worth a lot. If you don't have money to afford a really good set of wheels, just getting a duplicate of the wheelset you already have and just putting new tubes, new tires, and new cassette goes a long way towards ensuring you have a good race. Even if you are just a rec rider, having a second wheelset you use only on group ride days might be worth it to ensure your equipment problems don't hold the group back.