It would be angsty because Kaiba would be a very angry drunk, and also because Yami would probably be a very mopey drunk. Also, anything that would drive Kaiba to drink enough to become drunk would have to be very unpleasant indeed. It would probably end up a fist fight.

But also possibly end up with them moping on each other and cuddling. It's hard to say. Maybe after the fist fight.