No. Kinect is a motion sensor/camera—it cannot connect to Xbox Live directly. You need an Xbox 360 controller for Live navigation, dashboard use, and almost all gameplay.
To Use Xbox Live on 360
Wired or wireless Xbox 360 controller.
Stable internet connection (wired recommended).
Kinect Enhances Gameplay but Doesn't Replace the Controller for Live
Motion/voice controls in supported games (Kinect Sports, Dance Central, Mass Effect 3).
Voice commands for dashboard navigation ("Xbox, go to...").