Not on the first gen, however, I had no use for the app and deleted it after the first time I played with it. My plan was to download the app whenever I wanted to do something, then immediately delete.

By default the button is set to use voice controls with your phone. The app let's you make it do anc controls

When you buy a new pair these days, pressing that button causes the headphones to say "Configure the action button in the Bose Connect App"