It is possible yes, however I have not found any mention on the forum of anyone having tried it. The feature is not yet built-in to the web interface.

I am in the process of assembly. Once completed I will start working on how to set up recording manually. Others will have to decide if it should be a feature available in the web interface. Video capture has not been as high a priority as passing leak proof 300' depth test etc.. Most users have been doing video capture on the surface vial their laptop.

The specifics of how the software works can be found in the github section. Of interest is that they are using a linux utility called mjpg-streamer to send jpeg stills from the webcam to the web browser. The streamer can be set to create two simultaneous streams one to the website and the other to a file location. The question is what are the appropriate settings, high resolution mode will use more CPU and in addition one may need to transcode the video to MP4 for instance.

The implementation might be something similar to the solution found here: Raspberry Pi Security System

/usr/bin/mjpg_streamer -i "input_uvc.so -d /dev/video0 -f 10 -r 960x720" -o "output_http.so -p 80 -w /media/share/www" -o "output_file.so -f /media/share/cam1 -d 1000" -b