You don't even need to log in – just visiting a URL sends it to google. I'm not sure if you can even disable that despite all the predictive/protective/suggestive checkboxes in config – I couldn't figure out how to stop my dev domains from being leaked to google until I moved to chromium.
Keystrokes are sent to your default "search provider", so if you configure chrome to point elsewhere it will send your keystrokes to someone else. You can add custom URLs as "search engines" so just put in a non-existant domain, or DuckDuckGo, and it won't tell on you.
Or being logged into Chrome.