Can a Fallen Angel or Ascended Demon become a Fade?

Yes. Just about anything can become a Fade. Fallen or Ascended would retain, however, the markings of their wings, and the mark of The Mourning Star upon their person. Neither can be removed. They would, however, lose the ability to recognise other fallen/ascending and their purpose that was given by The Mourning Star as they would no longer be Fallen/Ascended.