Is it possible to publish/broadcast the video file which doesn't have audio file like screen recording?

No, it's impossible.

The video file which contains both audio/video files can be encoded as of current specification. So it's impossible to publish/broadcast the video file if either of them is missing on that file.

▼Example・If adding the video file which doesn't have audio file by "Add VOD", the error - "There is no audio stream in the mezzanine file. Please check your file and try again." is displayed and encoding is failed.

Please prepare the video file which contains both audio/video files by adding audio file by video editing software if you want to publish video file which doesn't contain audio file, and try "add VOD".