It does, after years of using a wireless controller I borrowed a wired controller from a friend and noticed a difference right away. The reason for this is because since a wired controller is wired directly into the Xbox, there is absolutely zero latency between your action on the controller and the action on the screen. A wired controller has a slight delay. The difference is not big, but you'll notice it if you've used a wireless controller for a long time.
The average human does not have the ability to perceive any difference between the two, if there is even a difference to begin with. The difference between the two in latency is not that significant. Truly, the only real advantage to a wired controller is that you won't have the batteries run out during play.
Perfection. Where everyone fails. If you expect nothing you can be happy for everything.
The difference only matters for PC games where you need to make a series of extremely fast and accurate clicks. And even then it's iffy. Certainly in a game like Halo, the difference is negligible, and probably unnoticable altogether