The shortest question I ever asked:
Is it possible that a friend from my friends list is selected by random as an opponent in ranked mode? Or are friends avoided in the selection? Does it make a difference, whether the friend or me is invisible or not?
Best Answer
There is no sure way to face a pre-determined opponent in ranked mode. That's the simple answer.
However, it is not impossible to do so, just generally quite unlikely. There are more players at lower ranks than at higher ranks, so it is less likely to happen at low ranks and likelihood increases at higher ranks.
Anecdotally, I have accomplished this in Arena mode once. My brother (RealID friend on Battle.net) and I had both drafted arena decks. We would time our entry in the queue to be as close as possible. After a few tries, we actually did get matched against each other, but weren't able to do so again. It really just comes down to a bit of timing and a lot of luck.