It will likely depend upon if your primary insurance physical damage coverage of collision or comprehensive (whichever coverage would be used depending on how the car was damaged) pays out a claim for a total loss of your vehicle if your GAP insurance would make a payment.

GAP insurance normally only comes into play if your vehicle has been declared a total loss and you receive actual cash value (ACV) for your vehicle as a settlement from the insurance company. At that point GAP insurance would be used to pay the difference between ACV and your loan balance still due.

If your car was not totaled out or if it was but you are not receiving ACV for it then it would be doubtful that your GAP insurance could be used in any way. If instead your car has been declared a total loss and you are receiving actual cash value for it, then your GAP insurance will also likely pay out. To be certain you would need to check with the terms of your GAP policy and/or check with you GAP insurer to see if they still pay out if someone not on your policy wrecked the vehicle.