Does car insurance cover the driver if he is not on the policy?

It may and it may not. It depends on the definitions of an "insured" driver under the terms of your insurance policy and the type of insurance policy you bought.

Most standard policies will extend coverage to certain drivers you have given permissive use while others such as low cost "Named Driver" policies extend coverage to no one other than those named on the policy.

Contact your insurance agent if you need assistance with your policy language.