I think you should be more specific with this question. What part of the Christian Tradition? Which Christian Tradition? I would suspect that the significance of Jesus is not dependent on any or all traditions since the significance of Jesus is, on one level, totally person ... it comes from an encounter with Jesus on a personal level and is different for each person.
However, it is clear that the Christian tradition has had a powerful impact on history and the significant of Jesus in that history. Starting with Constantine Jesus Christianity moved from an "underground" religion to a state religion; Jesus moved from a personal relationship to a state relationship, and everything changed after that "moment." In the name of Jesus all kinds of things happened, some of them good, many of them not so good. This created the historical Christian Tradition and presented the significance of Jesus in a way much different than the early days of Christianity.
I'm not sure if this answers your question. Please update with additional information if it does not.