Here I take an image (above) and apply global saturation -100
Now I'm going to add a graduated filter with saturation -100. Obviously it does nothing to the image, as it's completely desaturated:
Less intuitive is that when local saturation is boosted to +100, the net effect is not saturation 0 (which would make the picture half colored). It seems that the global effect is applied last, and in a different stage:
Local adjustements, instead, will sum nicely (given that they do not exceed a reasonable parameter range). So here +100-100 = 0. If you overlap more adjustments, then the +100 are eventually going to overflow, so there's no guarantee that the final result will be nicely predictable:
As it was pointed out on the thread, local saturation is additive with color saturation. So we can bring all colors down to -100 and restore them locally with a graduated filter/adjustment brush:
Now the inverse experiment: graduated filter with saturation -100.
Moving slightly global saturation from 0 to +100, you can see that the saturation affects the grey part of the image. (you would need an animation to see it, but it's really evident if you try; anyway in the grey part of the first image here, there's more white).
But the issue is even more complex.
As pointed out in this book, for example, some sliders will apply a different algorithm for different ranges of parameters (e.g. positive and negative clarity). So if the total value of the parameter is not "consolidated" between the various sliders, there's no guarantee of what the final effect will be.