The Xbox 360 camera needs a USB 2.0 port to work on Macs. I had the camera plugged into my AGP 400MHz G4 tower via it's built in USB 1.1 port. It didn't work, I installed a USB 2.0 PCI card and plugged the camera into that and, boom! Works great under the latest version of Tiger. 🙂
So as long as your eMac has USB 2.0 ports, and you're running the latest version of Tiger - you can use the Xbox 360 camera just fine. Just remember, the camera does not have a microphone, but the eMac (and most other Macs) have one built-in or you can use an external microphone.