If you enable the check box in Preferences > General > Display color management, it will adjust the colors on the Source and Program monitors according to that monitor’s associated .icm file. However, this is only for viewing purposes on that specific monitor.
For an eyedropper to work properly, it must sample the color as it exists BEFORE color management is applied to it. But most of the eyedroppers inside of Premiere will only sample a color AFTER it has been adjusted by color management.
You can prove this by turning on color management, then trying to use a Color Matte’s color picker to match something else with solid colors. The results will always be different. (As shown in the image with the color bars.)
Currently, the only way to properly sample any color is to turn off color management first, as I demonstrate in this short clip. (45:41 to 46:21)https://youtu.be/QPubgoqtfbk?t=2741
Currently, only the eyedroppers inside the Lumetri Color effect work correctly when color management is enabled. (As far as I know)