I wouldn’t have thought so. The parts are prohibited, so you will need to purchase them properly, but I think the serialised part of the weapon is the frame and firing group. Changing barrels is pretty normal, and lot of manufacturers make a kit to convert a 9mm to a .22. (CZ for example) the barrel and slide are useless without the frame and firing group. Either way you still have one gun with one serial number.
I thought about doing this, but the dynamics are different, and 9mm isn’t that expensive if you buy in bulk from someone like Belmont, or reload. Let us know how you get on.