If you mean by cumulative that when an opponent draws one card, you can pay three mana and thus draw three cards : No
Here the wording would have been: If an opponent draws a card, you may pay

, if you do, draw x cards.
If you mean by cumulative that when an opponent draws three cards, you can pay three mana and thus draw three cards : Yes
Three cards drawn (like Ancestral Recall) is actually worded as: Draw a card, Draw a crad, Draw a card.