Chrome adds it's own repository on install. On https://www.google.com/chrome/browser/ it states:
Note: Installing Google Chrome will add the Google repository so your
system will automatically keep Google Chrome up to date. If you don’t
want Google's repository, do “sudo touch /etc/default/google-chrome”
before installing the package.
So unless you do that before you install it should add a repository that will keep Chrome up to date with the system upgrades.
Picture of my sources after deb install:

So yes you will get updated versions of Chrome when doing updates. (either through Software Updater or apt-get update and apt-get upgrade)
So no intervention required if just do your updates like normal, I suggest letting it do them daily, as the update process is less intensive with only a handful at a time, and there are no forced restarts, and the old version of a program can stay in memory while it is currently being updated - so it is be perfectly fine to have programs open while they are being updated.
google-chrome-stable
. > installed it via the PPA. – ashes999 Oct 14 '14 at 03:04