Regarding the system - maybe not, except situations where you have some special features on it, e.g. a game, which needs users to click around the content quickly, and some clicks may occur in the very side of it.
However - since usability in general is about making the system reflect user expectations better, it gets quite important. I believe most of the users have some sense of balance, and aligning the layout to one of the sides abuses the feeling of a website being balanced, this making it - in user's perception - not perfect. This may lead the user to perceive it as "worse" and "less handy", which is very close to being less usable.
On a second thought. As a right handed person I prefer to keep my cursor in the right part of the screen. It may be silly preference, but it is so. So, moving it to the left part of the screen is less handy for me. This becomes even more important on tablet. I ususally hold it in/on my left hand and operate it with right hand. So, the more to the left the content is, the more I need to move my hand. At some point it becomes important.