Possibly. I am not licensed in Kentucky, but I am familiar with the process in the states where I am admitted. Most states have mechanic lien laws - where a person does work to a vehicle and is not paiod, the law requires the garage owner to give notice to the owner. Notice may also have to be given to the Department of Motor Vehicles. If the vehicle is not claimed, then the garagemen can sell the vehicle or can have the police have the vehicle towed away.
My advice would be to check out the Kentucky lien law as it applies to repair shops as well as the abandoned vehicle law. I would comply with the requirements of your state so that you can lawfully sell the vehicle and recoup what you are owed.
If you just haul it to the scrap yard, you do not have title to the car and you are opening yourself up to a possible lawsuit from the vehicle owner for conversion.