[Clipper]

No. Dogpile isn't even a target for Annihilation at that point as it should have been discarded after it resolved when all the monsters were added. Annihilation can only be played on cards that have just been played or cards that are in play.

Note that if the player had chosen to use Annihilation while or just after people were adding monsters, it would cancel Dogpile and everybody would take the monsters back into their respective hands.