When something shows up on a report that you didn't inform the insurance company about, the insurer will re-evaluate if you're an acceptable risk. You may still be offered a policy, but your rates could change from what you were originally quoted. One minor ticket may not change rates much, if at all, but if it's a major offense expect your rates to jump significantly or the offer to disappear altogether.
If you already purchased a policy, then when the insurer finds the “forgotten” information you may be notified that your premiums were modified due to this new data and that to keep your policy in effect you will need to pay an additional premium amount. If you don't pay the extra cost, the policy will cancel out. Or you may just be informed by the insurer that it's canceling your policy because it now perceives you to be a high-risk driver that they don't want to insure.
State laws on cancellation once a policy is started vary, but one typically allowable reason is misinformation on the application. Intentional misrepresentation can be seen as insurance fraud.
If your rates go up, or your policy is canceled after your insurer finds the missed speeding conviction, then shop around to get the best car insurance rates possible -- and this time make certain to provide insurers complete information. (See " 12 ways to double-check your savings.")