The traveler has no effect.
The logical flaw is that with n > 2 blue eyed people, everybody knows that there is at least 1 blue eyed person AND everybody knows that everybody ELSE knows that there is at least 1 blue eyed person.
The traveler's comments would only have an effect with n<=2 blue eyed people. With n = 1, he'd instantly know. With n = 2, the 2nd blue eyed person would recognize that the first person now has the information and if he doesn't commit suicide on the first night, then the 2nd blue eyed person knows the 1st blue had the information before, meaning he saw somebody else, and then they both die on night 2. n > 2, the info is already out that blue-eyed ppl exist and the count has already started.
The traveler's comments would only have an effect with n<=2 blue eyed people. With n = 1, he'd instantly know. With n = 2, the 2nd blue eyed person would recognize that the first person now has the information and if he doesn't commit suicide on the first night, then the 2nd blue eyed person knows the 1st blue had the information before, meaning he saw somebody else, and then they both die on night 2. n > 2, the info is already out that blue-eyed ppl exist and the count has already started.