If you're really just playing music or listening to the radio over wi-fi, your battery will last longer. However it got trickle charged while on the radio dock from 56% to 74% while playing the radio.
What about when you are reading a document or a book on your phone for an hour with brightness set to 30 or 40%? How is your battery doing? That's what I do on my phone 70% of the time, reading PDF docs files or books.