I don't know about the alcoholism angle. He has several blackouts in the novel, but we also see him turn down booze frequently. I would have liked more elaboration on his past. I saw the alcoholism as a product of his new life along the river. Remember his initial blackout in the novel? It seemed like binge drinking was something almost new to him.
To my reading, Suttree abandoned his wife and son purely for freedom. He abandoned predictability, boredom, stability, narrowly defined roles and attitudes, and everything about a plodding pre-mapped trajectory that his upbringing and marriage were delivering. He simply freed himself.
I think his depravity and the separation from his family runs much deeper than that, and is a narrative driver of the novel. You know that Suttree is held responsible for the boy's death by the family when he tries to go to the funeral. You know Suttree holds HIMSELF responsible when he won't let anyone else bury the boy. He didn't directly kill him, but he certainly ruined the lives of his loved ones and the boy's death is held as the ultimate result. The beginning of the novel is a fade-in of what he is, not what he became. He's always been a drunk and has always denied being a part of his wealthy family. You can look at the river as a metaphor for life (trite, I know), and he lives in a falling-down shack on top of it, pulls his meager living from it. When he leaves it and wonders briefly in the mountains he even goes through a severe withdrawal episode. The book is ultimately about the way Suttree separated from commonality and acceptance, but there is nothing beautiful about what he finds in his freedom and in the end there is nothing that he likes. I'm being very short, the themes are myriad from race relations, crime and punishment, religion, social responsibility and on and on. I never read McCarthy because he's easy. In fact, I read him because he's not. Suttree is, in my opinion, his best, although that's somewhat like picking a favorite apple from an orchard.
I asked myself the same question as I read the book. I tried to rationalise Suttree's rejection of his past life and family by imagining what his back story might be and whether there would be any single episode which triggered his later behaviour. The novel is set in the early 1950s and I picture Suttree as being in his late 20's or early 30's at this time. This would put him at the right age to have been involved in WW2 in some capacity. Perhaps he was witness to some atrocities in that campaign and consequently returned suffering from what we would now recognise as PTSD. I am sure there were many veterans of D-Day or the war in the Pacific who came back as deeply troubled and changed individuals and Suttree could well represent that constituency. Alternatively he could just have been a latter day slacker who had rejected the conformity of 1950's America - rather like other literary heroes of the time. I wonder what would have happened had a hitch-hiking Suttree been picked up by Dean Moriarty and Sal Paradise in one of their road trips at this time?