Yes you can!
On your Viewer device, tap the camera icon at the bottom for recording during live-viewing sessions. You will see a circle on the lower right corner to signal a clip is being made. Tap the camera icon at the bottom again, and you can find the clip in Moment (the cloud icon next to the main menu). You can record for as long as 30 seconds!
On the WebViewer, click on the film icon to start recording:
You will see a timer popping up. Click on the film icon again when you are done.
You will find the recording (as well as everything you have saved in your Moment folder) in the Moment section!