If Bringer of Dreams and Nightmares Repeats a Power, can the Repeat "destroy" Invaders that were "destroyed" by the original Power use?

If Bringer of Dreams and Nightmares Repeats a Power, can the Repeat "destroy" Invaders that were "destroyed" by the original Power use?

Yes. The Repeat is considered a separate action from the original.
This also means Bringer's Repeat cannot usefully combine Damage with its original – for instance a Repeated "2 Damage" Power couldn't do anything to an undamaged City. The original action would resolve, and 2 Damage isn't enough to destroy the City, so nothing happens. Then the second use of the Power resolves, and 2 Damage isn't enough to destroy the City, so nothing happens.