But, if you taped it with an interrupted spacer that allowed air to port out, that problem would be solved, no?
Meanwhile, I don't think it would launch the bullet all that far.
Out of curiosity, I did a quick look-up on powerheads, also called bang sticks, used by divers against sharks. (My thought being that they are in some ways similar, with a cartridge held at the end of a spear in the case of the powerhead, to what the OP suggested.)
The killing mechanism of the powerhead, though, isn't the bullet itself - it's the high pressure gas forced into the shark at contact.
Loosely extrapolated, if one could rig the cartridge to the BB gun muzzle, using an interrupted spacer to allow the air ahead of the BB to port out; and if one were to press the weapon against the bad guy while firing the BB into the primer, this might work.