While an interesting theory (I should read the book), how are you certain that system 2 comes online when viewing the timeline?
One example in the book is that even hard to read fonts can cause cognitive strain and make you judge the content of the text differently. I see that as being largely analogous.
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?