Yes, once you "pair" your smartphone with the Aftershokz, you will hear EVERYTHING that normally comes out through the smartphone speakers through the headphones. This applies to all Bluetooth headphones as far as I know.

You can also control the volume with buttons on the Aeropex. Buttons are a little small, but work.
I think it's app specific, but at least Spotify I can set to "pause" or "next song" with a button on the headphones. Hugely important for me when I'm on the bike and have my smartphone in my backpack.

So the headphones cannot be used as an antenna like cable headphones used to be if that was the question, otherwise everything that the smartphone plays on other headphones is played, but can also be used on the computer if Bluetooth is available.