I've not needed to use this Task in my implementation so far, so I'm not familiar with it's behavior. Being a Educational/Enterprise entity, we have enough control over the endpoints already that we don't get much resistance from the Users about having the BES Components running on their systems. In fact, most of our users are professionals and LIKE having the BES Client installed and running because it means that they can get the software/patches they need without interruption to their work day.
From what I can see, you are correct, the Task does not look for a scheduled task to determine relevance.
It simply targets systems that are running newer versions of Windows with BES Client v8.0 or newer and have the Scheduler service running.