If you choose to enable Search Across Computers, Google will securely transmit copies of your indexed files to Google Desktop servers, in order to provide the feature. Google treats the contents of your indexed files as personal information, in accordance with the Google Privacy Policy.
Your copy of Google Desktop includes a unique application number. When you install Google Desktop, this number and a message indicating whether the installation succeeded are sent back to Google. Also, when Google Desktop automatically checks to see if a new version is available, the current version number and the unique application number are sent to Google. The unique application number is required for Google Desktop to work and cannot be disabled.
Extras from Desktop Privacy Policy.
If you choose to send non-personal information about your use of Google Desktop Search, the unique application number with this non-personal information also helps us understand how you use Google Desktop Search so that we can make it work better.
Google Desktop Search uses the same cookie as Google.com and other Google services. If you send us non-personal information about your Google Desktop Search use, we may be able to make Google services work better by associating this information with other Google services you use and vice versa. You can opt out of sending such non-personal information to Google during the installation process or from the application preferences at any time.