Had another poke around and is still intrigued. I took a 7-speed cassette and held it to the 6-speed.
If I line the cassettes up small-to-big(for easy visible comparison) by the time I reach the 5th sprocket, the 7-speed is entirely "inside" the 6-speed sprocket.
Can't imagine that this shifter + derailer would index cleanly on a 7-speed system on more than a few sprockets at a time. The specs - which state 5.5 vs 5.0 mm spacing - certainly match the visible impression.
It seems possible that a 7-speed standard Shimano cassette would fit the freehub body, although I haven't tried it. A 7-speed ought to be wider than a 6-speed, but I'm not seeing any obvious spacers taking up room on the freehub body.
The use of that extra click in the shifter still eludes me. Maybe a derailer with a different amount of pull would let it run a 7-speed cassette.
Or it's like that "ghost shift" bug/feature some DT shifters had.