You're dreaming. You'll also expose to Google IP and website URL via Referer in requests for fonts and jsquery bundles, in Google cookies masqueraded as first-party via CNAME tricks, in Chrome identifier and so on. Chances are you're using Google DNS 8.8.8.8 too.
I wont trust a company to disable the data source for their main revenue. Just don't use any of Google software and services. Android included, sadly.