Yes you can. It does not need to have a registration that is active or even a license plate on it. Since the car is on a carrier and not on the road, you don’t need to have it registered.
The best way to look at it is to consider brand new cars coming off the factory floor. These vehicles are not titled or registered. They are only being carried to the dealership to be sold. If the carrier was to flip over or crash, the vehicles would be covered.
Shipping without registration is fine but keep in mind if a vehicle is not registered it probably isn’t insured or has limited insurance (storage, etc). So be sure to check. As a result, there may be coverage you’re missing out on.
Remember, the insurance covers the exterior of the vehicle due to damage caused by the carrier. But if there’s a hail storm or some kind of weather event that causes damage to the vehicle even while it was on the carrier, it is up to your regular insurance to cover such damage commonly known as “acts of God”.