Technically true, but the smaller the standard deviation of the radius (relative to the mean), the more closely the distribution of masses will approximate a normal distribution.
So you might say that the radii = r + e, where r is constant and e is normal around 0 with variance way, way smaller than r. But then the volume of the ball bearings = K * (r+e)^3, and because r >> e, the largest source of randomness term is going to be 3Kr^2e, which makes the whole thing look pretty normal.