Impossible to say, really. I think it would've all depended on whether he would've had that breakthrough film or radio role. When he died, he was making a good living as support comic relief in MGM features, and I could see him doing that until the end of the studio system. If he did find that breatkthrough performance, then I guess the sky would've been the limit.
Still, he DID have a bad alcohol problem, and while it would be naive to think all successful Hollywood people were sober, we'll never know what kind of effect this would've had on his career had he lived.