Google has a track record of pushing out Google-y spyware through software update channels. Whatever assumptions you're making based off Android's *current* behaviors, it's not safe to assume they'll hold.

https://news.ycombinator.com/item?id=18064537 ("Chrome 69 will keep Google Cookies when you tell it to delete all cookies")

https://news.ycombinator.com/item?id=24817304 ("Chrome exempts Google sites from user site data settings")

https://news.ycombinator.com/item?id=20044430 ("Google to restrict modern ad blocking Chrome extensions to enterprise users")

https://news.ycombinator.com/item?id=17942252 ("Tell HN: Using Gmail? You will be force logged into Chrome")