I think that you should find everything you want to know about slings and slingers on this page (which makes special mention of the Punic Wars, with quotations of several relevant sources).

While I don't know of any actual tests done, I've held one of these slingstones in my hand and they could certainly inflict some pretty serious damage. Especially if you consider that the armor worn during the Punic Wars wasn't anywhere near as good as during Caesar.

Slingers were definately used, and in rather large numbers. Polybios, who fought for the Romans during the 3rd Punic War, has described their use in Hannibal's army, which you can read about here and here. He doesn't seem to mention anything about them in effect though.