Yes. When you are live streaming with Save Video While Streaming turned on, you can pause the local recording. The live stream keeps running while the recording is paused, and it continues until you stop streaming.

To turn on Save Video While Streaming:

1. Open Settings and turn on Enable Live Streaming.
2. Tap Live Stream Settings.
3. Turn on Save Video While Streaming.

Under that option you can also choose Separate Start/Stop Buttons, which gives the recording its own controls independent of the stream. When separate buttons are off, On Live Stream Start lets you pick Prompt for Choice, Pause Recording, or Begin Recording.