No. We don’t normally mix cars with our household goods shipments in case they leak or move and damage other items.
I suggest using a car carrier called Wallenius. They operate whats called a roll on roll off service where you can drive your car to the port. They drive it onto the ship, secure it and then drive it off the ship at the destination ready for you to clear through customs and collect it.
You are not allowed to put anything in the car, UPakWeShip can ship any boxes that you may need to ship overseas.