If you reorganize your uploads into folders with Real Media Library, the plugin will only create a virtual folder structure. Therefore, Real Media Library will not change the URLs of your uploads in the wp-content/uploads/ directory (and could not break links of already used uploads).
But you want to Physically reorganizing your uploads and want to have changing URLs? Please read the following article to learn how you can achieve that: How can I reflect the virtual folder structure (physically) in my file system?