The Gen Kill party pics do show Alex in full party mode, but I keep in mind that according to James Ransone as well as Alex, he only went out twice in 7 months, even though all his castmates were out almost every night, partying. The rumour that first went around was that Alex was stuck up and didn't mingle with the others. Ransone said Alex simply was either working, and he was in more scenes than anyone else, because his character interacted with every other group, or he was at the hotel working with his dialect
coach.
Being able to focus like this when everyone around you is letting loose doesn't suggest to me Alex has a drinking problem, even if he does let loose when he decides to party, which I think he probably does--Ransone did say the two times Alex went out, he was party animal. It sounds like his way of drinking is pretty common in Sweden. If the drinking starts to crash his relationships or his career, he's got a problem, but I haven't seen anything in his public life that suggest he's anywhere near Kiefer Sutherland, Alec Baldwin or Jonathan Rhys Meyer territory, all of whose drinking has resulted in public incidents. Alex did put his days of blacking out and waking up in the woods in the past tense, not the present.