It would if you held the bullet in a collet, including a specially made one from one of the soft steel Morse taper mandrels you can buy. Few drill chucks are quite as concentric as is desirable for this job. I'd prefer metal to wood to hold the drill, clamped firmly in place, and start the hole with a short, rigid centre drill. Then I would epoxy the drill into the hole. I have drilled Morse taper reamers for a pilot with carbide drills that way, and end mills to make a bore reamer piloted on the long operating rod and pulled instead of pushed.