From my reading of the book (and the exerpt you have mentioned here), I'd agree that System 2 is in play when looking at the Timeline; it does create some cognitive load.
However, I can't remember anything backing your assertion that System 2 is more susceptible to advertising. In fact, my reading is the opposite: System 1 cannot help but read words or look at images, and it is easily swayed by various advertising techniques. It would be System 2 that processes what's happening, realizes you are trying to be sold something that you probably don't want/need, then rejects it. Isn't it a lack of engagement of System 2 that leads people to instinctively click ads or follow spam links?
However, I can't remember anything backing your assertion that System 2 is more susceptible to advertising. In fact, my reading is the opposite: System 1 cannot help but read words or look at images, and it is easily swayed by various advertising techniques. It would be System 2 that processes what's happening, realizes you are trying to be sold something that you probably don't want/need, then rejects it. Isn't it a lack of engagement of System 2 that leads people to instinctively click ads or follow spam links?