Difficult to describe exactly what happened, but best as I can...
- Mac Pro 08 running El Capitan; all else up to date.
- Plugged iPad into a USB cable coming via the wired keyboard.
- Mac screen went entirely black. Mouse cursor was still active, but no keyboard input would be accepted - any command would give the 'oops, wrong key command' beep.
- As far as I could tell, all apps were still running correctly, behind the scenes, though the only real evidence was that the internet radio was still playing in Safari.
Unplugging the iPad made no difference.
Prime consideration - I didn't want to hard power-off the Mac, risk losing work &/or [this has happened before] not being able to boot up until I'd fiddled with Disk Warrior/TechTool etc
Incidentally, the iPad shows as Not Charging. I haven't yet investigated whether this is because it's connected through the keyboard rather than directly.
I need to do further research to see what may have been the cause, but I'm going to post an answer myself as to how I got out of the black screen, in case it's useful to others...