From Into the Wild, is it possible that taking the family dog with him would have had any effect on Chris's journeys?

This question comes from second-guessing and hindsight. Chris's sister Carine explains that their parents, Walt and Billie, believe that the presence of Buck the dog would have caused Chris to act in a more cautious manner; since Buck had been recovering from an accident, they believe that Chris would have been more careful and perhaps not gone so far into the wilderness.

"My parents can't help wondering -- and I admit that I can't, either -- how things might have turned out different if Chris had taken Buck with him. Chris didn't think twice about risking his own life, but... there's no way he would have taken the same kind of chances if Buck had been with him."
(Krakauer, Into the Wild, Amazon.com)

This question is entirely up to personal opinion. There is no way to say one way or another if Buck's presence would have affected Chris's journeys. In fact, if Buck was sufficiently endangered, it is more likely that Chris would have left the dog with one of the many friends he made during his trip. Perhaps Buck would have had a grounding effect on Chris, but by the time he left Emory, Chris had cemented his personal philosophies and it is unlikely that he would have changed them for the dog.

On the other hand, one of his favorite authors was Jack London, who wrote tales about man and dog against the wilderness. It is entirely possible that with the dog to "help" him, Chris may have ventured even farther into the wilderness, thinking that he was reliving the sort of experience that created London's famous stories.