Maybe he will out grow it, but ask yourself, does my son look any different at this age than a kid who will not out grow it? Do you have any way to tell, other than a pediatrician telling you that he would, and at that, said "most likely"? What if he is one of the few that will not?
Make an appointment with a speech pathologist and get him evaluated. Get the therapy, and find out for sure. In this day and age, doctors will send our kids off for medical testing at the drop of a hat if they suspect the rarest of disorders, to protect themselves from malpractice, but they routienly tell parents to wait and see for developmental concerns that can be effectively treated with early intervention. Why wait to see when you can have an answer and know for sure? Is it worth the risk that he might continue to stutter much longer than he might if you got therapy? And think about this, what is the worst thing that could happen, if you get an unnecissary evaluation and the therapist tells you that he has no issue and it will absolutley go away? Wouldn't it be worth it? You have far more to gain, than you have to loose.
M.