I know SR3 didn't have it, instead it had like a mixtape option for the extremely limited soundtrack options in that game (Which were some Rap, some Rock, some Metal, some Trance, some Techno/Pop, some mixture of stuff from Adult Swim.)
In order to add your own tracks you have to mod in a radio station. (A Jet Set Radio station would've been fantastic to make for that game.) Which is something that's probably time consuming.
I'm not even sure about SR2 but its broken as hell on PC so I wouldn't even bother with that.
EDIT: Aannd San Andreas just locked up on me. Beautiful.