Yes I have seen that done too & even have an MT3x1.5? arbor to marry my BH to tailstock socket. I have yet to try it but its on my list.
Some precautions:
- the BH is set ideally level but more importantly remains in same position during turning
- the BH does not rotate on its arbor adapter
- the MT shank doesn't rotate within TS socket
- lock the BH gib once set so its kind to the BH displacement under side cutting force
One thing that doesn't get a lot of mention is that when you drill a 60-deg center in stock & then position it offset in TS on a 60-deg point, it can become a problem at increasing taper angles. Its best to use a parabolic center drill so the dead center cone is tangent on the surface.