Is there a duplicate of the egg or Anivia or nothing at all?
Never tried something that weird. :)
If the egg isn't destroyed, nothing will happen. The check whether Anivia dies or is rescued by some ability happens before (when the egg is created). So her passive will begin it's cooldown no matter what and she'll be reborn.
If the egg is destroyed, I assume one of the other effects might trigger again. This is something that might actually work even if you're unable to apply any of the other effects to the egg. Just imagine Guardian Angel ending its cooldown just before the egg is destroyed. That sounds like something really interesting (and complicated) to test though.
Possibly important: I'm quite sure you'll get an Anivia Spirit if you're using Mordekaiser's Ultimate on her and the egg is killed. So I'd just say the same is true for Yorick's Ultimate (once the egg is destroyed).
Either way: You won't see a "Revenant Egg" or something like that. The champion is still Anivia, so you'd end up with an Anivia Revenant.