As I understand it's not going to be updated entirely, but how about security patches ? I have thoughts that using Chromium is better for privacy (if compare to Chrome), but it is drawback in security.
Chromium is in the official Ubuntu software repositories and is updated like everything else in the OS. See Chromium's Launchpad page.
That means, that all relevant security fixes are available as package upgrades through Canonical's
security repository – either in form of a completely new version of the software (like for Chromium) or a so called "backport" of the security fix to the version currently released by Canonical (like for core system libraries or the Linux kernel).