FWIW, I do not use anything other than an empty but foiled water pan, however .....
There is (could be) a benefit to putting a stone in there: Assume you foil the bowl. Then, you place the stone in, and again, foil on top of that. Any dripping fat will fall in to the bowl as is normal but not settle on the very bottom, since the stone will be raised up creating an air gap. The (potential) benefit here is that this dripping fat will not burn from high relatively direct heat of the fire below it, thereby making the smell (and potential taste) more pleasant.
I essentially do this when I foil the bowl by either putting a few tin foil balls in the bottom or simply foiling such that there is a gap between the foil and the bowl bottom.
This would be of particular use if you have a new WSM with the stock deep bowl.
YMMV and all that.