You dont say what your small mill is or how much torque is needed to drive the vertical axis, also without knowledge of the motor specification you dont know whether it will do the task, and very importantly how long for.
Maxon make a wide range of high quality motors some with precious metal brushes, ironless rotors and other features to enhance performance for specific applications. I am not conversant with Maxon's part numbering but if you go to a lot of work to use this motor and gearbox and it fails after a short time, a replacement motor will be expensive. It would definitely be best to do some investigation and experiments before you go to far.
For you to consider this application in the first place I presume the gearbox has a substantial output shaft?
Ian P