No, there is no certainty that if Bob had not gone to the West he would not have turned out to be a criminal. The West didn't make him a criminal. He went there because it seemed to offer opportunities for criminal activities. He tells the plainclothes officer who asks if he did well out West: “Bully; it has given me everything I asked it for."
If Jimmy had gone west with Bob, Jimmy would have ended up in some strictly respectable and secure profession. Their characters were already formed by the time that Jimmy was twenty and Bob was eighteen. Bob would have looked for excitement and opportunities to get rich quick in New York if he had stayed in that great, ever-growing metropolis--and no doubt he would have found plenty of both.
Bob characterizes both Jimmy and himself when he says of his old friend, "He was a kind of plodder, though, good fellow as he was." Jimmy is a plodder relative to Bob, who has the character of a gambler. If Bob had stayed in New York, he might have been less successful as a crook because there would have been more competition in every racket. But he would have grown in the same direction, and the friendship between the two men could not have survived. In actuality, it did not survive even when they were separated by a thousand or more miles. Jimmy did not realize that Bob was no longer his friend until he encountered him in the doorway of the drugstore after twenty years. Their friendship might be said to have "gone up in smoke" when Bob lighted his cigar and Jimmy saw his face. In that instant they became "erstwhile friends." Their relationship was based on the fact that they used to be friends. Jimmy couldn't remain a friend of a man like Bob.