Unless the smart car is unregistered, I doubt it, as there is an £80 fee to swap the registration on your car.

It is a right ball ache waiting around for all the forms to come through, but it is worth it in the end!

My tip would be: Once you have your V5 document for the smart car, go directly to a DVLA office (if you can) as if you mess up the forms, you can simply fill out new ones.