Question about some Special Abilities

[Poryhedron]

I was thinking recently about the Special Abilities Huge Power and Pure Power, that would basically be identical to having twice as large an Attack stat if not for the effects of Trace, Role Play and Skill Swap. Then something occurred to me: if these Special Abilities do the same thing as a single Swords Dance without the used-up turn, does Haze remove their effect? (Obviously pseudohazing wouldn't, since as soon as you send them in again, the Special Ability takes effect again.) And how about Compound Eyes, which is basically the same as using an X Accuracy without the used-up turn?

[Don't Run With Scizors]

Nope, the effects of those abilities can't be Hazed away. Just Skill Swapped.