Yes, your GAP insurance would cover the difference between you physical damage insurance company payment and what you owe on the car. GAP insurance only pays the difference between the actual cash value and the amount due on the loan. If you had GAP insurance and physical damage auto insurance on the vehicle, the physical damage would pay up to the ACV and the GAP insurance would pay the difference of between that and the amount due on the loan.

There are some restrictions on GAP insurance.

Comment Update (below): Unfortunately, new insurance would not cover previous damage to the vehicle and GAP insurance will only come into effect if your vehicle is declared a total loss.