[Conway] did invent a game using Go equipment known
as 'Football' (I recall it being quite playable but I've long since
forgotten the rules),
"Phutball", or "Philosopher's Football". It's described, eg,
in "Winning Ways", with advice on how to play decently well. It's
computationally v hard, so difficult to play really well!
apparently he came across a Go set before he knew the
game and realising it was game equipment proceeded to invent a game using
it before asking anyone about it.
Possible but seems unlikely; he would surely have found a
use for all the unwanted black stones [white stones in the colour-
reversed version described by Wiki].