Young Australian Country singer Catherine Britt got her start exactly that way.

She was at a concert which featured Bill Chambers, father of Kasey Chambers. The 12 year old asked Chambers to do a particular song. For whatever reason, he said he'd do it if she'd sing with him. Britt didn't have to be asked twice, climbed up on stage and the rest is history. Chambers liked what he heard, helped her get started, and the now just-turned-18 Catherine Britt has signed with RCA, has been on the Grand Ole Opry, sang a duet with Kasey Chambers (That Don't Bother Me), is slated to do a duet with Elton John, etc., etc.

Just found the quote. "I just went over to him and asked if he could sing TV Blues, I was 12 I think, and he said 'only if you get up and sing it with me'. He had no idea I was a singer, just thought it would be really cute to have a 12 year-old up there singing TV Blues with him. He says he was blown away by my performance, which is really sweet, cause I'm a huge fan of his"