You must let the company know (and your parents) that your license is suspended. You cannot drive or be insured on their policy with a suspended license. You could be putting your parents or their policy at risk for non-disclosure.

The company can pull your driving record when they try to add you to the policy. They can disclose that they are not able to add you because of your driving record. They can give the inquirer information to use in order to contact the reporting agency.

I think you know what you need to do.