He'll take it the second time it's offered to him. He just won't want to be the first one hitting it.

Okay, okay I wanna know what the Alex drinking game is! Haha. 

Logan will laugh when she says she's not crazy, watching her and Billie.
Zach will give a relaxed smile. "It's fine...."
Logan will interrupt him. "He'll be more social and laxed when he drinks some." And he will pass a shot to Zach before pouring Billie and Clary a shot. 
Zach will down it. 
And Logan will be like. "If I knew we were playing that, I would have gotten here sooner."

(Haha is there a party they have that doesn't end up like that?)