Unlike some other screen recorders, Dashcam does not upload your video to the cloud until you click the Publish button. Instead, Dashcam records to a local directory, and the video is quickly uploaded after your review.
But you're a developer, and you want to see for yourself. If you're on Mac, Little Snitch is a handy tool to monitor Dashcam's activity. While it won't allow you to see the individual requests and responses (thanks HTTPS), we can infer some things about Dashcam's activity just by the size of the data transferred at different times.