Yes, a palmed ball can indeed be reflected. If using shiny cups certain moves and angles sometimes have to be adapted at close quarters.
To expand a bit on my above post :
In my mind the focus of a Cups and Balls routine should be the balls, not the cups. So the balls should always stand out more than the cups. Im not saying the cups should blend into the background and be barely visible, but at first glance the balls should catch your eye more than the cups, which are merely covers. It should be the same for the mat or table covering, which should be dark and inconspicuios. The magicians dress should also be taken into account. Ideally you wouldnt want something bright - when the balls are on top of the cups (or to quote Paul Daniels ''the top of the bottom of the cup''

) you want them to stand out from the background (your attire).
Using shiny cups runs contrary to this. The way that the light bounces off a shiny cup draws your eye to it rather than the ball.
I use a similar philosophy for other effects. Take the Coin Matrix for example. Same idea - the cards are there as covers for the coins - the coins should be the focus. For this reason i use a dark mat and blue backed cards. The blue cards are not as bright as red and dont stand out anywhere near as much against a dark background. My coins, which are shiny and bright are in stark contrast to the cards and mat, and the eye is immedietly drawn to them.
Of course the cups and Balls can be done very well with shiny cups, and any cards can be used for Matrix. I just feel this sort of attention helps with the focus and clarity of effects, and also sets a nice picture
jim