Yes, with a few caveats. For iOS users, when you record your gameplay, your party audio is also recorded so you can relive all your epic moments.
Android Users Please Note: PlayStation has DRM protected content, and recording this content will result in a black screen. For recording PlayStation games, we recommend to use Playstation's built-in screen recording in the PS Remote Play app and share that content through PSN.
Android Users Please Note: While using the "record gameplay" feature, only Party Audio output is recorded. Input from external devices (e.g. Microphone) will not be picked up.