Thanks to Matteo Scaramuccia, a particularly helpful and brilliant Moodler/PHP developer, and this initial forum post, we now have at least one alternative way of hiding the user (admin, teacher or student) on the Online Users block (by Andy J. Davis).
It's all on my blog and hope this helps you and your teachers.
In short, you can now be invisible. You can, if you wanted to, also display your avatar on the Online Users block with a displayed status like, "(away)", "(busy)", "(ready to help)", "(chat with me)". The possiblities are endless.