I would imagine it's the opposite, as formulae generally require the input of tangible, quantifiable parameters in order to work.
That said, I've worked under both good and bad managers, and I do believe different people in the same role can make a difference to outcome, to a certain extent. However, there isn't a manager in the game who can be given an outfield rotation of Pillar, Carrerra, Goins, Valencia and Colabello and produce a collective that excels both offensively and defensively. There isn't a manager in the game who can step in and make Dickey excellent again.
I believe that there is a possibility that someone could be brought in who may be able to do a better job of motivating, or a better job of holding players accountable for poor execution, or , but I also acknowledge that any gains in this area may well be negated by someone who knows less about platoon advantages, or is more careless with outs.
In my opinion, targeting Gibbons as step 1 in righting the ship only delays the inevitability; the realization that this team isn't deep enough outside of a core of 8-10 guys or so to maintain the kind of consistency required to go on a run that makes this team relevant.