No, I don't believe the new Visual Editor has the ability to easily see the URL path to the image. If you have it set to media link, you can see the URL in the edit window, but if you are scaling the image ( or have it linked to "None" ), then nothing will show there either.
If you don't want to switch to the Text Editor, one way would be to simply right click on the image in the Visual Editor and choose your browser's "Inspect Element" (or equivalent) option. The full file path to that version of the image (if scaled) will show in the
src attribute of the
PS - I don't really remember if the old Visual Editor had that ability, either. ;)