Is there any web-service API capable of achieving the following task-
An admin/authorized personnel should be capable of marking a course as COMPLETE for all of its users regardless of the passing or failing of its participants
The list of course web service API functions can be found here: https://docs.moodle.org/dev/Web_service_API_functions
There doesn't appear to be anything matching what you describe, the closest is core_completion_mark_course_self_completed, but that only works for the current user. It may be a useful place to start if you want to implement your own function for this.