Yes, you can save your Swivl recorded project to your Camera roll IF it has not yet been uploaded to Swivl Teams. Such a project has a red icon next to it.
Projects already uploaded to your Swivl Teams account cannot be saved to your Camera Roll. They have a blue cloud icon.
See how to enable/disable the Auto upload feature in C-Series Robot & Swivl App Settings - iOS Devices
There is no option to save your video to the app gallery (video will still be accessible in file explorer)