Considering the fact that you need 7,777 GC clicks for the "Black cat's paw" achievement, I think Cookie Storms should count towards that goal. Before you even make it to 1/4th of that number you can be so close to end game that clicking GCs (and active play in general) is a waste of time, especially with Spontaneous Edifice. It requires an unreasonable amount of attention given to this game of which idling plays a large part.
Personally, I find it to be just as bad as the building level achievements. The arbitrary timers make it a chore to get these achievements, but at least you can idle for Sugar Lumps.