But you can still store trackers right? Just not cross reference the tracking cookie with the cookie from other domains.

I can see this if you go from site X to site Y where you're logged in on both X and Y, and you can correlate (say) the email. But if you're logged into Y (the store) but not X some random referrer, how do you attribute the conversion?

You will be kindly asked to log in with Google everywhere, for your convenience and security.