If the car purchased is in your name then you can add it to your own insurance policy in your name. In the event that the newly purchased car is in your son's name then the car insurance policy will need to be in his name. That way if he gets pulled over for a traffic stop or is involved in an accident there will be no question about whether or not the vehicle is fully covered by insurance.
After your son does lose his license the insurance company will likely cancel any car insurance policies in his name. Every 30-90 days insurance companies review their customer's driving records for any changes. He probably won't be dropped immediately often times it will be after the current policy term is up. Written notification of insurance policy cancellation will be sent through the mail unless you specifically have selected to only receive electronic notices.