I got a Chinese drill press a few years ago, and it came with pre-failed bearings. They were noisy from the first, and the spindle had to much run out for doing any work even close to the tolerances you folks are discussing here. I replaced them with a good set of bearings and did the proper pre-loading etc. and it has worked OK. Even so, at best it can be used for some polishing, or minor side loading.
There are some small metal lathes, and small mills available normally from the same source as the drill presses (like Harbor Freight or Menards) that for a few bucks more will do what you want, and even do more. I recommend you consider one of those prior to spending the money.