Do Powers that cause Ravage Actions (e.g., "Manifest Incarnation") check if any Invaders are participating in Ravage, just like Invader Cards do?

Do Powers that cause Ravage Actions (e.g., "Manifest Incarnation") check if any Invaders are participating in Ravage, just like Invader Cards do?

Yes. Those Ravages only include Invaders that can participate in Ravage.
Though it rarely matters, the Ravage Actions caused by Power Cards don't happen if no Invaders are able to participate.