The color picker found in the Add Global Color dialog dialog only picks colours in RGB, independently of the document color space.
Steps to reproduce:
Create a new CMYK document
Create a new object on the page, for example a rectangle with C:0 M:0 Y:0 K:20
Open the Swatches panel
From the Swatches panel flyout menu, chose Add Global Color
Use the color picker found next to the drop down menu to pick the color from the rectangle
Notice the color value is expressed in RGB rather than CMYK
Thanks!