Of the above list (for NTSC, that is) only these songs appear in the races:
1. Apollo 440 - Cold Rock The Mic
3. The Crystal Method - Now Is The Time (Y2Kaos Mix)
7. Rob Zombie - Dragula (Hot Rod Herman Mix)
9. Garbage - Paranoid
12. Soul Coughing - Super Bon Bon
This one's only in the intro for the Arcade Disk:
2. The Cardigans - My Favorite Game
And I don't know about the rest of these; they might be on the "official soundtrack" that you could buy separately.
4. Hole - Use Once And Destroy
5. Creed - Unforgiven
6. Moby - Bodyrock (B&H's Bodyrob Mix)
8. Fear Factory & Gary Numan - Cars
10. Boom Boom Satellites - Push Eject
11. Filter - Hey Man Nice Shot
The Filter song made it to the GT2 booklet, but not the game.
Also, Beck - "Two Turntables" and The Foo Fighters - "Hero" are in the Ending Credits.