Connecting iPad 'crashed' the display - black screen but cursor responsive
Because I didn't want to hard power-off the Mac I had to do a bit of lateral thinking.  

I was quite sure that the machine hadn't actually hung, as the radio was still playing, but that perhaps something had upset the Finder, which I think was the frontmost app at the point the iPad was plugged in.

A moment of revelation... what about dialling in remotely?  

I went to my other Mac &amp; tried to get in via Screen Sharing.
Success... or not... I could share the screen, but it was still black with just a working cursor.  

What if I try to login as myself instead?

Joy!
Screen Sharing showed me the login screen.
I went to check the remote machine, it too was showing the login screen.
I logged the original user back in, rather than myself, &amp; we were up &amp; running again.  

I rebooted at that point, normally, &amp; the issue hasn't recurred.

I still have no explanation as to what caused it, but I hope this might help anyone else who sees a similar issue.