Don't forget an important point. Once the velocity exceeds 500fps AND the muzzle energy is in excess if a certain amount, it is classified as a firearm that falls under the firearm act. This means at this point, there are laws about how you can transport, store, and use. Also, a short barrel length and being full auto would prohibit it.
That being said, I don't know if the muzzle energy can reach that high with a plastic BB.