I don't have direct experience of DropBox, but in general, if you have the URL (Web address) of any remote file, including one in a repository, you can just link to it.
Turn editing on >> Add a resource... >> URL
For images and multimedia you can also use the appropriate buttons from the Editor toolbar, e.g.
Turn editing on >> Add a resource... >> Label >> [Inset/edit image] or [Moodle Media] button>> Find or upload... >> once you have selected the file from the filepicker, make sure you select the 'Link external' checkbox (to avoid copying the file).
You should also be able to use the usual Moodle filter 'tricks' to embed such remote multimedia links into a Moodle course.
Of course, this does require that the files in the repository are accessible from the Web, but I presume this is what you mean by a 'Public' DropBox folder.
Note that although it results in 'unecessary' duplication, copying, rather than linking to, the resource avoids access issues as the copied file inherits the appropriate permissions of the Moodle course it is in.
Otherwise, you may need a more complex setup with a repository such as Alfresco where you, in some way, align the roles and permissions in Moodle with those in the repository. As I understand it, systems such as Edu-Sharing, Elis or Joule 2 (I think, a hosted version of Elis) offer this kind of capability.
Note that some of the above may require a recent version of Moodle 2.x, I'm using Moodle 2.1.1.