No, the side connections are input only => either s-video or composite video, and stereo audio.
The easiest way to capture the component video feed from your XBox 360 is with the Hauppauge HD PVR [
http://www.hauppauge.com/site/products/data_hdpvr.html ] ==> This will record the component and audio signals ... and has a pass-through for both the audio and video [So you connect the X-Box to the HD PVR, and then connect the pass-through outputs to the TV.