NCF – Extended list of Neutral creatures.

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So, the effect doesn't move with the creature? And during the flight-jump, is the creature headless? And then the head returns to its place? On the new cell?

During the jump, there's a separate model. So, even if you give Fire Demons a jump ability from Elder Demons, the model will change to that of an Elder Demon during the jump and revert back upon landing.
The same thing happens with Ents; during the rooting animation, the model of an Ancient Ent changes to that of a new Ancient Ent, which has its own animation set.
Therefore, if you give Wild Ents the rooting ability, they will turn into Ancient Ents during the rooting animation.