most auto insurance policies are rendered void if the policy holder damages the vehicle during a 'speed contest.' since autocross is timed, and technically a speed contest, insurance won't cover it. interestingly enough though, trackdays are often covered, since they're not competitions -- ditto track schools.
my thought? you break it you bought it. don't burden the rest of the world with high insurance rates 'cause you wrecked while racing.

 

if i wreck it while racing, i just buy a better aftermarket part. but if you didnt do that, and wanted to scam insurance, there really isnt any way to know that you raced your car, you could make up some story about how it happened, its not like at auto-x days they take your VIN and report that to all the insurance compaies