Yes, independently replicated clinical trials show that it does work to get rid of stuttering. Clinical trials have also shown that it works in a telehealth version, where the speech pathologist and family actually never meet; the treatment is done either by telephone or, more commonly these days, with Skype over the internet.
Research has also shown that the program is safe. It does not appear to interfere with parent-child relationships and has no apparent effect on other aspects of communication. Indeed, parents report that their children are more outgoing and talk more after treatment because they are no longer stuttering.