No. The Kinect Sensor does not work on the original Xbox 360 "Phat" models (often called "Pro" or "Premium" — the white/grey consoles with chrome disc tray, 2005–2010).
Microsoft sold a Kinect AC Adapter (Power Supply) for using Kinect on Xbox 360 S/E when the console's internal port couldn't supply enough power (early S models) or for PC use. This adapter does NOT enable Kinect on a Phat 360. The Phat lacks the data lanes and firmware support entirely.
If you have a Phat 360: You cannot use Kinect. Sell/upgrade to a Slim/E model (cheap used) if Kinect games (Dance Central, Kinect Sports, Fruit Ninja, Child of Eden) are desired.