I enjoy food/drink pairing, but to my taste, no attempted pairing has complemented pipe smoke well besides
a medium roast Sumatran coffee with a Balkan tobacco.
Most other coffee/tobacco combinations tended to detract both ways.
A few other drink possibilities may be neutral, but don't enhance anything (water, tea).
But most other drink possibilities positively clash (any alcohol, IMO).
I don't see the need to drink anything while smoking a pipe.
Although I enjoy parsing a tobacco for flavor, like a food or a drink, I don't categorize tobacco with food and drink so far as pairing goes. For me, it's an evening enjoyment to be had on its own.
If I'm thirsty while smoking, I'll drink water, just like any other time.
(But again, I will admit that a medium roast Indonesian coffee and a Balkan mixture do really complementary things together.)