Yes, the teen driver is covered, though depending on the car insurance company they may need to be listed on the policy first. You should contact your insurance provider to verify whether the teen needs to be listed with a permit or if the company prefers to wait until they have their driver’s license.
For more information on this topic, check out this article: https://getjerry.com/advice/can-i-get-car-insurance-with-a-provisional-drivers-license-by-cheryl-knight.