Hi Malcolm, and welcome to Jag-lovers!
I know they exist, because I’ve driven one! It was a loaner from the dealer, as I recall either a 2016 or 2017 V6S AWD Convertible. Basically the same car as my 2014 V6S RWD Convertible, except for the AWD.
I remember two takeaways from driving that car for a couple of days. It felt noticeably less “peppy” than my RWD car, and the steering felt “wooly”. Less precise. The steering issue could be because Jaguar switched from hydraulic to electric power steering from the 2016 model year on, as mentioned by @Ole-XKE1974 in this post.
The difference in get-up-and-go was so noticeable that when I got back in my own car, my first reaction was “Whoa! Big difference, I sure wasn’t imagining things.”
As to how rare it is, I have no idea. It might also depend a little on where you are in the world? I live and work in Silicon Valley, where luxury cars are everywhere, but even here I don’t see many F-Types in general. That said, and knowing the locals, I’d imagine that most of the people in the market for an F-Type would opt for the AWD once it became available.
Best of luck in your search!
Regards,
Gunnar