When I try to import or open mp3's from my Dropbox folder using Rhythmbox nothing happens. I'm using Rhythmbox 3.2.1 and Ubuntu 15.04 64 bit. If I copy them to the desktop then they play, but my playlists are inside Dropbox, so I can share them between my devices. OGG files seem to work just fine.
Check the permission on your Dropbox folder. More than likely the do not have the execute permission enabled.
Cntrl + Alt + T to open Terminal
chmod ug+rwx ~/Dropbox
This will enable execution of files in the folder for your application.
Then, close Terminal and re-try your files with Rhythmbox.
Alternatively, you can open Nautilus and navigate to your Dropbox foler.
Right-click the mp3 file, click Properties, the select the Permissions tab. Be sure all users and groups have Read and Write Access.