Right now advertising is interrupt-driven. Could one do the opposite? What you are suggesting seems like a frontal attack and that may not be the best tactic.
What is the goal of advertising anyway?
For the ad-buyer, the goal seems to be increasing sales.
For the consumer, the goal is ... what?
When it comes to websites anything that diverts my attention from the page that I came to look at is going to interrupt me so I don't know if that's really a good criteria.
Take the easy case of a consumer ready to buy something this minute. Say, they want a colorful winter jacket for men, and they are willing to pay anything for it.
Can they find it with advertising? Can they find it with search?
One goal of advertising for the consumer is that it helps them make a decision. Which of these X jackets should I consider?
Now, is being interrupted the best way to make a decision?