The color picker must be hosted on a non-modal dialog such as a dockpane in order for the Eye Dropper tool to be able to be used. Set this property to true when you are specifically wanting to hide the Eye Dropper tool on the color picker; for example on your own custom ProWindow that is displayed in a modal fashion.
Note, the application may hide the Eye Dropper tool by default in some scenarios. For example the tool will not be visible if the color picker is on a propertySheet.