Yes, just like the first one I had when I was 15 years old.
To be honest, I think the car should staty with the tag and the re-body and if the new car is sold, the old car should go with it. Then the new owner will have the car. Why even go to the trouble to rebody the car then ? The thing to do would be to just duplicate the car for driving and keep the old car with the vin intact. That is done often for racing old valuable vintage cars.