If you have any music or audio notes playing on tape, CD, or whatever and you fall asleep, is it true that you'll have whatever was played memorized by the time you wake up?

I certainly wouldn't rely on this strategy to learn anything more important than a new French toast recipe. While I suppose it's possible to retain some of the information on your audio notes, you'll only pick up tidbits that you stored to memory as you were still awake. You absolutely cannot study in your sleep.
Even more important is this: When you're sleeping, any noise that differs from what you're used to will make you take longer to fall asleep and wake up more often. One of the most surefire ways to bomb an exam is to be sleep-deprived when you're taking it. Study, then get a good night's sleep, then review in the morning. You'll be much better off.