Ah yes the old ancient ball polishing machines I remember
them well at least the one we had in our center back in the
80's early 90's. It would always leave the ball spotty looking
at best, sometimes you couldn't even tell the difference after
a cleaning/polishing session as the ball would still always look
the same even with a new block of wax and new cleaner inside.

I'd have to say stay far, far, far, away from one of those ball
cleaning machines now days especially if you're using one of
todays high performance balls as others have said a plastic /
urethane ball might benefit from using one of them though if
you can not get it done in the pro shop.