Yes, the Lumia update (Cyan, Denim) brings the custom sounds for the reminders to the existing Windows Phone 8 devices.

To set custom sound for the reminders:

  1. Connect your phone to a PC with a compatible USB cable.  
  2. Browse to the phone folder of your Windows Phone using File Explorer.  
  3. Open the Ringtones folder (top level folder).
  4. Copy the sounds file from your PC into the Ringtones folder.
  5. In your phone, go to Settings > ringtones+sounds. Under Reminders, open a list and choose your Custom sound from the top. Tap on a play button to preview the sound.