That doesn't make sense. If you use Covenant w/ Noah on Abomination of Desolation after the phase it was placed, it would negate AoD for that phase. Now, would KoT do the same???
Example:
RA Thankful Leper w/ less than 10 cards in opponent's deck. Block with KoT. I play Meeting the Messiah on a character in his territory, so he has to draw 2 cards. Does abomination activate???