I'd imagine that even if they don't all get along, they can make it work on TV. Most of the morning shows are pretty generic anyway. Billy Bush is a professional just like all the others, for what they earn, there's no reason to think they can't all play nicely together.
Billy Bush will fit in well with the other members of the Today show when he appears on an episode. He has been featured on a few episodes before and got a long well with all of the members. He is also good friends with the cast of the show.
It is my opinion that the lighthearted and easygoing demeanor of Billy Bush will enable him to make a smooth transition to Today. I do not foresee there being anything abrasive or annoying about him that would agitate the current members or cause them to view him negatively. Billy should round out the show nicely.
Billy Bush will have a hard time fitting into the Today show. Although he was warmly welcomed, it is a tight knit group that has been working together for a long time. This is important to the show's chemistry, and the stars talk about their personal lives. Bush was criticized by one of the show's personalities, which will make it difficult to gel.