For a definite answer to your question if your physical damage collision coverage will cover this accident claim you will need to speak to the claims adjuster on the case and/or your agent. In general unless there were exclusions in your policy, if you gave your son permission to use the vehicle by you then it likely will be covered by your insurance.

You noted that your son did not live with you, thus was not part of your household which normally would have required him to be on your policy with you. If he frequently drove your vehicle you insurance company may still have required him on the policy as at least an occasional driver, so that may be discussed when the claim is being processed.

Since the car was determined to be a total loss, if the insurance company does accept the claim then the insurance company should next determine the actual cash value of the vehicle so they can settle with you for the car. Typically, a GAP policy only pays if physical damage coverage is in effect and the claim is accepted.

Please add comments to let future visitors know how it turns out.