Vic, hard to answer without knowing which one/size, etc, but… When I bought my lathe 10-12 years ago, I also bought an MT3 live centre, approx A$60 – 70 as I recall. It was a piece of crap, got graunchy very rapidly, had it replaced, same happened again, jumped up and down, they finally replaced it with a significantly more expensive Skoda, which still runs smoothly to this day.. I pulled the old Chinese one apart (just needed a standard pin spanner at the front) and all the internals came out as a single assembly. Thing is, the centre, which is the front end of the central shaft on which all the bearings are assembled, simply had an upset boss at the rear end which held everything together and simultaneously preloaded (overloaded) the thrust bearing.
The two main ball bearings feel perfectly ok (as they should, because it only had a few hours of use before the thrust bearing quit), but with the amount of work that you would have to put into it to try and make a decent device, the expression involving silk purses and sow's ears definitely comes to mind. I would suggest saving a few more quid and buying a Skoda, which I expect would also have other points available.
The only reason I have held on to my old Chinese unit is because (1) I rarely throw anything away, and (2), the MT3 shank and body might one day turn into a tailstock die-holder (if I wait long enough).
Roger