Yes they do. In fact if I comment out the problematic code and play the game, the sprites animate fine using the original clip, set in the inspector ("hatAnim").
If I change the default in the inspector to any of the other three clips, this also works.
Also, as I stated before, I can turn the sprites on and off in the script using "SetActive."
The sprites were created using "Create Other>tk2d>Sprite With Animator".