Yes it is possible.
I will show you, how to create a folder with a lock sign on it, that can only be accessed the original user or author, no other user can access it, even it is not in My Documents folder.
Note: All screenshots in all the tutorials are click to enlarge feature enabled. You can click them to see in real sized screenshots, after the page load is complete and a box appears around the particular screenshot.
For example, I have created a folder named The Customize Windows in E partition of my Windows 7 PC:
By right-clicking on the folder, select Properties and open the Security tab :
You can allow only to read, not to copy or even not to access/open the folder. After restart or simply restarting the explorer.exe, when an unauthorized user wants to open the folder, he/she will get this:
In the above example, I have made all users to be denied by the System to access the folder.