does Macbook Pro continue refreshing screen when brightness is set to zero? In other words, does my Macbook's CPU realize it is wasting its time and energy by continuing to send instructions to a screen that has been completely darkened by setting the brightness to 0%?  (Not sure if this is equivalent to "display sleep."  It may be.)

I would hope so, but my guess is that it ignores the brightness setting and continues sending instructions just like it does when the screen is doing something useful with them.

The reason I ask is because I use my iPad as an external display (via Duet Display) and routinely dim my Macbook's screen whenever it's hooked up.
Yes the screen keeps refreshing regardless of the brightness.
If you still have a mac with a glowing apple logo you can even see this,just dim the screen all the way and shine a light through the back of the apple logo, you can see the screen is still active in the light leaking through from the back.
Edit: since I can sense the follow-up question allready:
You can achieve what you want using one of the ways described in this article:
Stop screen rendering on macbook