No, the Guitar Hero 3 guitar does not work on Xbox 360.
Why
Different Technology: The Xbox 360 version of Guitar Hero 3 uses a USB connection for the guitar. The PS2/PS3 versions used a different proprietary connector.
Console-Specific Hardware: Even though the game shares the same name, the Xbox 360 and PS2/PS3 releases are separate with different hardware requirements.
You must purchase a Guitar Hero guitar specifically designed for the Xbox 360 to play.