The easiest way would be to create a new temporary KML point and to copy/paste values from the X and Y boxes in its Properties window.
If you are OK with the third party http://www.nearby.org.uk/, you could use their Network Link Echo. This KML Network link auto refresh after the camera stops and put a red X at the center of the scene. Right click on the scene where you want to obtain information and choose Near to center on this point. When you click on the red X, you will have every possible information you want about the scene. You can then copy/paste text from the popup window.

The hardest way would be to activate the ArcGIS Earth Automation API and to develop a tool that can fetch and copy the X and Y position of the cursor. You could do that with HTML, CSS and JavaScript, using the ArcGIS Maps SDK for JavaScript. Good luck!
Geoffroy Richer-Lalonde
GIS Specialist, Hydro-Québec