Apparently not. There's an ever growing tail of users who get stuck with an outdated version [1]. It's not as bad as Firefox yet but surprising nonetheless given how much effort Google put into Chrome's update system.
I have personally experienced and seen Chrome get “stuck” and kind of just fail to update itself until a manual re-download of the installer is performed. It does usually work, but sometimes just stops. For example, I recently saw a bug report from someone who thought they were on the most recent version of Chrome — 10. (It’s currently at 19 or so.)
[1] http://arstechnica.com/information-technology/2012/06/may-br...