I doubt it, as no single packet manager has delta updates, which is a crucial asset of their own solution.
More importantly, they have no control over what comes in and goes out of the repositories. I doubt Google would want to deal with every single distribution personally.
Google's solution for Chrome on Debian and Ubuntu is to distribute a .deb package that installs not only Chrome, but also installs a reference to their own package repository. When the user updates packages on their system, it updates Chrome from Google's repository. Chrome does not update itself, nor can it, since the package installs it to /usr/bin, which would require a su/sudo prompt to get access to.
More importantly, they have no control over what comes in and goes out of the repositories. I doubt Google would want to deal with every single distribution personally.