Yes, I can verify that Binaural Beats and Muse app can be used at the same time. I can hear the Binaural Beats track and the feedback sounds from the Muse app simultaneously. The standard Music app for the iPhone will not let you do this. Definitely not. Too bad, because I’d like to be able to listen to iAwake tracks while using the Muse app, and hear them both. Maybe there is a player app for iOS that will let you do this, but I don’t know about it.
For now, I play iAwake tracks on my Android tablet, listening to them with earbuds, while wearing the Muse headband and Muse app runing on my iPhone sitting nearby. I don’t know any other way to do it. But it is a bother to get all that set up.