Well, I've been coming back to this, every now and then, for almost 4 years now. The best I've been able to come up with is a block that is visible to instructors when they have editing turned on, but not while it's off. It's better than nothing. If anyone can make it work while editing is turned on, please let me know. I should add, though, that I've tried many, many different rights settings and they don't seem to behave the way you might think. For example, you'd think just setting a student to PROHIBIT and a TEACHER to ALLOW would work, but it doesn't.
In case anyone might find this useful, here's what I ended up doing:
1.In order to be a "sticky block," it has to be first created on the front page with a Page contents option of "display throughout the entire site."
2.Then enter ANY course and change the "Display on page types" option to "Any type of course main page." At this point, it disappears from the front page and can only be configured further from within a course page. However, this configuration takes effect regardless of which course it appears in.
3.Next, you have to edit the permissions of the block to remove access from everyone (yes everyone) to view or edit the block (Yes, I said EVERYONE. Adding the teacher to the View block access doesn't do anything, at all.). Note that while editing is on, anyone with editing rights to the course will still be able to HIDE or MOVE the block, but will not be able to delete it.