This effect activates even if your opponent controls more monsters with 0 ATK than you have cards in your Deck. In that case, you will lose the Duel due to not being able to draw enough cards.[1]
The destruction of 0 ATK cards and drawing cards are considered to occur simultaneously.[1]
This effect is activated even if you do not have any card in your Deck. (If 1 or more monsters your opponent controls are destroyed by this effect, since you cannot draw, you lose the Duel.)[2]