Only if the pilots and/or Trunk Monkeys involved are unprofessional assholes.
But really - it depends on the airplane how responsibilities and positions are divvied up. The difference between rank authority and positional authority is something that gets discussed a lot during CRM refreshers. In an E-2, for example, it's not at all uncommon to have a LT aircraft commander, LT NFO mission commander, and an NFO Skipper in back sitting ACO because being mission commander requires a lot of preflight mission planning and he's got Skipper shit to do. In theory the CAPC signed for the plane and he's responsible for it. But the Skipper owns the plane and he's also responsible for it. So if there's an issue, ultimately the CAPC will do what the skipper tells him to - but both will have to defend and explain their decision making later. If everyone's being professional, it'll be a collective decision everyone's comfortable with. What won't wash is someone saying "we're doing this because I'm the (x), end of discussion."