Uh, yeah, they do. Android is not as open-source as you think...
From Google's Privacy Policy (
https://www.google.com/intl/en/policies/privacy/):
"When you use our services or view content provided by Google, we may automatically collect and store certain information in server logs. This may include:
details of how you used our service, such as your search queries.
telephony log information like your phone number, calling-party number, forwarding numbers, time and date of calls, duration of calls, SMS routing information and types of calls.
Internet protocol address.
device event information such as crashes, system activity, hardware settings, browser type, browser language, the date and time of your request and referral URL.
cookies that may uniquely identify your browser or your Google Account."