Is There a Team Fortress 2 Demo for Xbox 360? No—Never Released

No. Team Fortress 2 on Xbox 360 (part of The Orange Box, 2007) never received a demo.

Why

• Valve focused updates on PC (Steam). 360 version got zero patches after launch.
• Xbox Live Arcade demo slots were limited; Valve didn't pursue.
• The Orange Box retailed at $59.99—no free trial needed for marketing.

Current State

• 360 version is abandonware: no updates, no matchmaking (servers down), peer-to-peer only
• PC version is free-to-play since 2011, constantly updated

If you want to try TF2, play on PC (Steam) – it's free, alive, and the definitive version.