I dont believe that Pepper will have any problem.
BB is a good manager. When you are a good manager, everyone knows where they stand with you. Mangini became the DC last year, because he was the next in line. Thats not a title, but something that is evident every day among a staff working together.
If BB chose Pees, I am quite confident that it was evident from the dynamic of the staff that Pees was a leader among them, knowledgable and impactful.
I would say, with no question in my mind (based on both the decision and the experience of each) that as LB coaches, Pepper learned from Pees and listened to his thoughts and advise and not the other way around.
There is never such a thing as equals among peers. Leaders emerge, some are teachers, some are students among themselves.
Pepper Johnson cannot feel bypassed in my opinion, if BB is a good manager who knows his people and lets them know where they stand with him.