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The critical factor is the location of the centre of pressure, which depends on the flowfield structure, which in turn depends mainly on the bullet's speed (supersonic or subsonic), but also the shape, air density and surface features. If the centre of pressure is ahead of the centre of gravity, the effect is destabilizing; if the centre of pressure is behind the centre of gravity, the effect is stabilizing.
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With a perfect sphere, both the center of gravity and the center of pressure are located together in the exact middle of the sphere, whether the sphere is rotating or not. In fact, since the center of pressure can never be ahead of or behind the center of gravity, the traditional meaning of "stabilization" as it applies to things like missiles and darts doesn't really apply to spheres. By the traditional definition, a flying sphere is neither stable nor unstable, regardless of spin.