No, there isn't any dedicated sound. As Rincewind said in 2006, you can hear when the player starts if you set the Start Screen to Resume Playback: You can hear the song that was running when you shut the player off the last time. Stopping playback is easy to hear and will lead to idle power off, in case the user accidentally does a short press of Power/Menu instead of a long press.
Also, if the Start Screen is set to one of the menus then you should hear the highlighted menu item get spoken if you have the voice interface enabled (to the best of my recollection).