I would say that is considerable play, especially if your guess is even close to accurate.
If there's play on the compressor side, there is also play on the turbine side, unless the shaft is bent, which it unlikely.
By up and down do you mean you can grab the nut and move it up and down (axial play). I would figure out what specs are for this turbo, get a dial indicator and check it. You don't want the turbo coming apart on you.
-R. J.