It will depend on state laws and insurance company guidelines if you will be able to insure and register a car before you obtain a license. The Department of Motor Vehicles, or like agency, for your state will be able to inform you of what documentation you will need to register a vehicle. In some states this may include a driver's license.
Insurance companies will prefer that you to have a license when you apply for insurance coverage on a vehicle. Some insurance companies will permit you to start a policy without a license if you are able to obtain a full license within a short time frame, typically 30 to 45 days from the inception of the policy. If the license is not acquired during this time period than your insurance would be cancelled.