An Xbox 360 keyboard cannot be used to navigate the Xbox Live dashboard or system menus. The console's interface was designed exclusively for gamepad input.
On Xbox 360, keyboards serve a niche purpose: text chat within supported games and specific in-game controls. They do not replace the controller for any system function.
If you need to type frequently (e.g., for Final Fantasy XI), a USB keyboard plugged into the console's front ports will work—but only inside that game.