If you do have a GoPro connected to an iPhone with Periscope, the footage will automatically appear within the app. You can switch between the action cam and the iPhone's camera. While you'll need to keep the application open to keep broadcasting, the latest update adds a lock screen switch so you can put the phone in your pocket while doing something awesome with your GoPro.
Recently Twitter timelines for iOS were updated to support livestreaming within a user's feed. Adding GoPro support has the potential to make the streaming service more of a destination fans of the X Games.
The update supports broadcasting and saving to the camera roll on on iPhone 5S and later. The iPhone 5 and 5c only support broadcasting. But the GoPros will save the footage to an SD card. So your epic backflip (or bail) is still available for later editing.