When a Power cares about how many Invaders that Power destroyed (eg: Mists of Oblivion, or Shadows' innate Power), do Damage boosts (Badlands, Flame's Fury) count?

When a Power cares about how many Invaders that Power destroyed (eg: Mists of Oblivion, or Shadows' innate Power), do Damage boosts (Badlands, Flame's Fury) count?

Yes. Damage boosts increase the amount of damage done, but the damage is still being done by the original source.