[Edi]

Generally yes, but remember that we're dealing with the limitations of the human body (structure of the wrist, arm and shoulder), so that puts a certain cap on how fast you can spin it. The thing that would most increase the power would be the length of the sling, since it increases the radius of the circle and thus the radial velocity or whatever it is you call the velocity of the stone as it travels along the edge of the circle before being released. There is a practical limit to how long the sling can be before the slinger gets entangled in it.

A slinging machine would not have to deal with the limitations of human body structure unless specifically built to simulate them.

The way you can test this issue is taking a piece of string weighted at one end and start whirling it like a sling. There comes a point where no matter how hard you try to increase the speed of the whirl, the increase in the speed is negligible. Try it with strings of various length. The speed of the whirling stone around the circumference of the arc and its mass are what determine the power of the sling far more than the strength of the slinger. A heavier stone will do more damage than a light one at the same range, but a lighter stone will travel a longer distance.