Does insurance cover the vehicle if the driver does not have a valid license?

It all depends on the policy. If the unlicensed driver is a named insured and the policy is active then they will be covered. If the unlicensed driver is excluded from coverage then naturally there is no coverage for them. If the unlicensed driver is not a named insured and also not excluded, Then technically they still are not a covered driver, although, coverege may still apply under the owners auto policy depending on the circumstances of any accident and the owners liability under permissive use rules if the vehicle owner allowed an unlicensed driver to operate the vehicle.