if his relationship with the dog had been different, do you think the man might have survived

The man died because of an unexpected attack from the neighboring Indians. The dog, by that point in the story, was often gone during the day and was not there to protect the man. That being said, Buck (the dog) could not have defeated as many Indians as probably attacked the camp, so it is likely that both Buck and the man would have been killed. The way the story ends, Buck goes off into the wild with the wolf pack after leaving John Thornton in the water.