No that's not normal.
I'm looking at an opened TC right now and don't see how the front output flange could be moving 3-4mm. The flange is locked into the gear behind it, which is meshed to the transfer gear. One of those gears must be very worn too. I just can't see how just a worn bearing could allow 3-4mm of movement.
Change the fluid and see how it looks, or better yet get a new magnetic drain/fill bolt from BMW if you don't have them. The bolts I recently bought from BMW were magnetic and had a 17mm head. My stock bolts were 16mm and not magnetic. My old TC was damaged externally, but was in perfect shape and had no metal on the bolts when I drained the fluid for the final time. The fluid was changed at least 12 times on that case. The replacement case was purchased used with "low-miles" and a warranty. It's had a modest amount of metal shavings on the drain bolts at each of it's three fluid changes so far.