Yeah, plus, since in the movie they were on the same team, and were in command positions, they had to interact. In fact, there is a clear indicator in the movie they have lines of communication, since it was Darjeeling who came up with, and organised, all the other schools to come to Ooarai's rescue. In fact, Saunders was the very first school she and Pekoe contacted, via wireless telegraph (despite being in a universe that has mobile phones...), they even conspiratorially called it a "tea party". To be honest, it is highly probable all the school leaders of these top teams interact with each other, with the possible exception of the Finnish school, they seem to keep to themselves.
Looking forward to the movie series, considering how some of these pairings got popular, I wonder if we will see some winks in this regard. If yes, Darjeeling/Kay is practically guaranteed.