Yes, your GAP insurance should pay out if your car is declared a total loss from an accident that you were not at fault in and thus which you are making a third party claim against the at-fault party's insurance.

As long as either your insurance company or the at-fault driver's insurance is paying the actual cash value (ACV) of the vehicle then your GAP insurance should then kick in to pay the balance of your loan or lease. If there was not an insurer paying the ACV to the lien holder then GAP would not normally be used since it pays the difference between ACV and the balance due on the vehicle, the "gap" amount when you owe more than your car is worth.

The at-fault party's insurance company will only pay ACV, also sometimes referred to as fair market value, since that was what your car was worth at the time of the accident. The insurance provider for the at-fault party will not pay off the loan amount in full, just the ACV amount. Insurance companies, whether you are putting in a first party or third party claim, will not pay you more than the worth of the car in the condition it was in prior to the accident that totaled it.

If you have put in a claim with the at-fault party for the damages to your vehicle and are negotiating a settlement for the value of your car, make sure to inform your GAP insurer so they are aware of the situation and can start your GAP claim. There are usually specific time periods in which you must get your GAP claim made within.