I think you should go ahead on that bike, but keep in mind:

1. does the race have a lot of hills?
2. is it really technical or just a sunday/sat morning ride?

if its a ride with a few rolling hills, then you should do just fine, given that bike is ~5lbs over what most carbon bikes are, it doesn't really matter THAT much unless you are going to be doing a lot of climbing.

if the race is a technical corner crazy crit, then i'd still go on that bike, but make sure you are fully re-acquainted with its handling and knowing what gear to be in, etc.

tires sound fine, and wheels should be fine too.

you WILL feel a difference with more modern wheels, fewer spoke count, lighter materials, but watch the gearing.

my bianchi feels far more alive with its 12-21 8-speed cassette, than it did with the 13-25...6-speed.