I don't think Google uses GNOME in any of their products.
But GNOME Desktop has an option to integrate Google services into the desktop environment. For example automatic syncing user's GNOME calendar to their Google calendar. Also it can sync email, contacts, documents, photos and even printers.
https://lifehacker.com/a-beginners-guide-to-the-gnome-desktop-1820890109
Also, GNOME Desktop has native Google Drive integration.
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