A while ago, when I used to sleep with headphones on listening to the radio, I would often dream of listening to music. One time actually I happened to be dreaming when the morning talk show came on, and it got incorporated into my dream albeit it somewhat warped. So yeah music can definitely transcend into your dreams. As far as inducing anything, I'm a noob so I really can't say much. But I do know that association can be a powerful thing for your mind.