You can play them on the 360.
I was doing it yesterday. But with a usb flash drive, not an ipod.
but It'll work just the same.
First you have to be connected to Xbox Live.
When you plug in the ipod, you have to go to the media blade, click on the Videos tab.
You'll see Console, Computer, Compact Disc, and Portable Device. (or something like that).
try playing the portable device, and it'll prompt you to download a free update that enables ipod playback for the MP3/AAV music files, or MP4 video files.