Yes, but it does not "move" the global slider.
No, it doesn't but to does move it 'under the hood'.
To better understand the workings , set the global settings to maximum
Amount 150
Radius 3
Detail 100
(Masking 60) - that's to refer to a secondary point later, not essential for this example.
Draw your radial Mask ( not a mask but a 'selection, in reality)
Then play with the Sharpness slider - what do you see ?
The selected area is being 'increased/decreased' ... even past the maximum 150 (try switching the visibility of the mask on/off with Global:150 and you'll see the effect)
So, if you had a setting of 40 in the global and you used a setting of +20, that would be the same as having the setting be 60 in those areas
...those areas being
the area selected by your 'mask'.