You'll only ever retrieve Google AMP cache results from the Google search page, where they were already able to track if you made such a request, since the link you clicked has trackers in it.
So from that perspective, nothing changes.
> PS: You work for Google. Do you work on this project?
No, I work on mostly internal infrastructure. My interest in AMP is simply that I don't dislike the AMP "experience", it's fine. But more importantly, I legitimately don't get the HN hysteria around AMP. Returning to your concern, literally nothing changes with AMP vs non-AMP.
I don't get it. The most compelling concern I've heard is that it's annoying to have to couple parts of your infra to AMP-standard stuff. And I sort of understand that. But even that isn't different than previous SEO/ranking changes that required changes to the page.