I agree that there is no diagnosis of insanity, but I think a case could be made for bipolar disorder (aka manic depression). It seems that Poe had periods of enormous creativity followed by bottoming lows. He also had a habit of writing about the "double self," thus lending credence to the belief that he felt torn between two existences.
Some of his behavior was quite odd as well. I recall reading in his biography that when his wife (and 13-year-old cousin) died, he had a strict ritual of walking around her grave a certain number of times each night, perhaps indicating OCD (obsessive-compulsive disorder.)
Of course, it's impossible to diagnose after-the-fact, but many depressives tend to self-medicate with alcohol, perhaps temporarily relieving his pain but ultimately exacerbating his condition.