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:
- Connect your phone to a PC with a compatible USB cable.
- Browse to the phone folder of your Windows Phone using File Explorer.
- Open the Ringtones folder (top level folder).
- Copy the sounds file from your PC into the Ringtones folder.
- 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.