Well...not directly. The mechanism that produces aurora is controlled mostly by the solar wind and by the ejection of large clouds called 'coronal mass ejections' from the solar surface. Sunspots are not directly involved in these two phenomena, but only serve to show the relative level of solar activity which does correlate with producing aurora. When the wind is agitated or when more of these CMEs are being spawned in a given time, the sun is in its 'active' state which also includes more sunspots on the surface. The brightness and color of aurora are pretty much controlled by how energetic, tangled, and magnetically active the solar wind and CMEs are as they impact the earth's space environment. They can shake loose and accelerate more energetic particles in the earth's environment, and these flow down into the polar regions to produce more, or less, dramatic auroral storms.