Given what slings are like, it wouldn’t make much difference. Combining values that I found cited for flight distance for top ancient to classical-era slingers and weights and shapes for sling bullets and plugging them into this simulator Projectile of a Trajectory: With and Without Drag | Desmos (I’m not that good at differential equations yet) suggests that at a range of say, 20 m (it doesn’t matter much between 15 and 40), the sling bullet would have been traveling at about 110 m/s, and had a kinetic energy of about 1300 J. Given that it probably weighed about twice as much as a baseball, and baseballs to the head at half that speed (or golf balls at that speed) can be fatal, and that that’s about as much energy as a .40 caliber pistol round, I doubt that anyone would remain conscious after a short-range sling bullet to the head.