Any highlight and shadow recovery done with the gradient tool or the brush will be in addition to any adjustments that you may have done globally before activating the tools. I'm not sure what you are really asking.
If we were to compare the following settings on two virtual copies -
1st virtual copy) 100% shadow recovery done with the global adjustment
2nd virtual copy) No shadow recovery at the global level but 100% shadow recovery by the brush tool.
Does the area covered by the brush tool in #2 match the same area in #1?
I have never concerned myself with that. I'm curious to know why it matters.
I had assumed that recovering highlights/shadows would be the same for global and local panels. But now I'm not so sure. In my testing the global shadows adjustment "seems" to do a better job with contrast as it recovers the shadows.
Interesting -- I would have (naively) guessed there wasn't a difference. But a simple test shows there are small but noticeable differences.
Start with an original photo. Make two virtual copies. In one copy, apply the global shadows +50. In the other copy, apply the adjustment brush with feather, flow, and density = 100 and automask off across the entire pic; then set brush shadows = +50. Export the two virtual copies as 16-bit TIFFs into Photoshop. Stack them as layers in a single image. This lets you see small differences just by enabling or disabling the top layer. With my test pic, I can clearly see small differences.
To quantify the differences, set the top layer's blending mode to Difference, merge the two layers, and invoke Image > Adjustments > Levels to see the histogram.
Here's my original test pic:
And here are the differences as computed in Photoshop:
As you can see from the histogram, the differences are in the range of 5 parts out of 255. They are greater in the shadows than the highlights.
Here's a Dropbox folder with the original raw and the two exported TIFFs.
It may be the feathering you applied to the brush. Have you tried this with no feathering?
Also, did you have Auto Mask selected? If so, there may be parts of the image that were not fully selected.
As described above, I applied the adjustment brush with feather, flow, and density = 100 and automask off. I had the largest brush size selected and had turned on the mask color ("O") to ensure the entire image was completely brushed, so feathering shouldn't make a difference. But I just repeated the same settings but with feather = 0 and got the same results.
This is just a guess but maybe the Global adjustments are adaptive relative to the whole photo and the Local adjustments are not.
That does sound plausible.
One thing to check would be the flow and density settings on your adjustment brush.
Flow controls the amount applied for each brush swipe of the area, the swipes are additive (2 swipes at 20% = 40% total).
Density controls the max amount of applied effect where Flow stops adding, normally wanted at 100%.
Once again, as described above, I applied the adjustment brush with flow and density = 100, automask off, feather first = 100 and then 0. I had the largest brush size selected and had turned on the mask color ("O") to ensure the entire image was completely brushed.