If a car has full coverage and someone else is driving the vehicle without a license will the insurance still provide coverage?

"Full coverage" is usually interpreted as meaning that it is covered for both physical damage and liability coverage.

When an insurance policy is purchased, among the factors that are considered by the insurer in accepting the risk is the make and model of the vehicle, the location at which it is principally garaged, the number of miles driven, and importantly, who will be the main drivers. Without question, any insurer will require that any driver of the car be licensed to drive.

Therefore, the broad answer to your question is, no.