Is it really the most popular? It's a plugin for a $1000 CAD program which seems to dramatically limit who can use it.

Yes, it has by far the largest user community.

If you do a google image search for 'grasshopper geometry' or 'grasshopper architecture', you'll see a lot of buildings designed with grasshopper, including many which have been constructed.

There are other interesting things going on, like automated construction with robots or laser cutters. For example, theverymany builds massive organic structures out of laser-cut metal pieces, and the living (new york) did some interesting things with robotic placement of bricks.

New design tools specialized for automated manufacturing methods.

Rhino is the cheapest professional CAD tool on the market by an immense margin.

Compared to Solidworks, Inventor, Studio Tools, Catia or any other package, a grand is a steal.

And compared to the horrific productivity of "free" cad packages, you will quickly recoup that cost. (aka Fusion360/TinkerCAD , SCAD)

Do you find Fusion 360 productivity horrific?

I haven't used the expensive programs, but do a lot of work in 360. Would love to know what I'm missing.

Is there a way to get it to work under Linux?

This is the first time I've heard of Grasshopper. Are you referring to this?

http://www.grasshopper3d.com/

How would you recommend a 3D printer operator could learn more about Grasshopper? Are the tutorials good?

Check out the grasshopper primer. I haven't read it in a while but I used to claim it was written by programmers for non-programmers. Great getting-started guide. Rhino probably still has a demo available, too. Dynamobim.org is another option if you want to try visual programming without an investment. Dynamo is mostly visible for it's connections to other software, e.g., Revit, but can stand alone as in sandbox mode.

EDIT:Yes, it's that grasshopper https://www.rhino3d.com/6/new/grasshopper for a demo reel