As long as you request the correct permissions you should be able to write to the SD card.
If you store the notification mp3 in /sdcard/media/notifications
(create it if it doesn't exist) and rescan for new media then they should show up in the notifications list.
Rescan for new media:
scanFile(Context, filepaths, mimetypes (optional), callback (optional))
See http://developer.android.com/reference/android/media/MediaScannerConnection.html#scanFile(android.content.Context, java.lang.String[], java.lang.String[], android.media.MediaScannerConnection.OnScanCompletedListener)