Yes you can play backup games on the 360, but it involves a firmware flash of your xbox360's DVD drive.
This tricks the 360 into thinking it's reading an original game.
There will almost certainly be a fightback from microsoft over this.
This is also not very safe for users of Xbox live as this hack may well be detected.
Leaving you open to prosecution or banning of your machine to future games or services.
Please see this website for further info:
http://forums.xbox-scene.com/