If it's a brand new shell and you use all new components to build up the car and you have all the receipts including one from the manufacturer of the shell (not from some guy on ebay) then you can get current reg.

If it's used to rebuild a car with a damaged shell and most of the components are from the original car and you have the receipt from the manufacturer of the shell, then you probably will get to keep the original reg.

Otherwise no.

And what's wrong with a Q reg?

Have I covered all the possibles?
.