We have some folders on our website which are password protected through a PHP script. Will Google or any other bot index files inside that specific directory? The files are accessible if you know the direct link.
www.site.com/files = directory is password protected. www.site.com/files/image.jpg = directly accessible without login.
Will Google index the image file?
Would you like to buy the Brooklyn Bridge? I can get you a great deal on that... :-)
Seriously, Google will not add your GMails to their index, nor use them to find secret URLs. If there is no way for Google to find your pages through links, Facebook posts, tweets etc., they will not be able to index them.
If you want to be absolutely sure, simply put a robots.txt file in your protected directory. See http://www.robotstxt.org/orig.html for more on the Robots protocol.
Good luck!