No, normally gap insurance does not play a part in an accident claim if the car was not declared a total loss by the insurance company involved.

Gap insurance pays the difference between the balance of your loan and the actual cash value paid out in a settlement for a "totaled" vehicle. If the car is only damaged and totaled out by insurance then the ACV is not paid out and thus there is not a difference for gap insurance to fill in and pay out.

If a car was damaged in an accident then you should use your collision coverage to place a claim for the cost of the repairs.