It doesn't seem like this would materially change the information Google receives. The status quo is that Google knows (via redirect links) what search results I click and when. It doesn't technically know what data the website will send me, but normally it's the same as Google's cached copy. It doesn't know what resources my browser will block, but in a bundle scenario, my browser is free to ignore resources even if they must be transmitted as part of a bundle.

> using the persistent tls socket can follow the users activity

Even if this caused browsers to keep idle sockets to Google alive more often, what information is there to be gained from an idle socket?