As far as I know you don't get the pack if you do the brawl with a friend. I play EU.
I'm on NA and got the pack playing with a friend. You can complete pretty much every quest playing with friends, and get brawl packs that way. Only exception is if it's a quest requiring you beat solo content bosses for a pack, or the "Watch and Learn" quest to earn a pack. In fact, the "Watch and Learn" quest... you can watch a friend win a game in a solo player game of Dungeon Run, or in any solo player game mode. A win against the Innkeeper in training mode even counts. When people ask me to do it I go to start a new Dungeon Run and just beat the first boss in 2 mins and they get their pack.
Each brawl has its own MMR, much like casual mode. The more you lose, the worse the players you are matched up with. Since this is a co-op brawl, worse "opponents" leads to more losses, which lead to even worse opponents. Eventually you'll have dug yourself into MMR hell and presumably be matched exclusively with 10 year olds who cannot read
That's why people are sharing such different experiences on this thread. How it goes all depends if you can win in the first few games, otherwise you are likely screwed :)
Been doing it for more then an hour, and no luck either my co-op player didn't know how to do it, or just getting screwed over by the mechanics of the game. Had to do it on a couple of other accounts, but after the first hours-try I gave up on all.