My cynical take on the whole culture thing is that yes, winning makes it's own culture. At the very least, you have to have some sort of success to show the players that the new coaching staff knows what they are talking about.
After years of losing at this point, with a couple of really long losing streaks, I think the new coach has to get some early wins otherwise I can see players, fans, and media just going, "Here we go again" and start to tune out the coaches as just being full of shit.
IMO, it's one reason why most of the Belichick coaching tree sucks elsewhere at HC for the most part. They tried to bring that Patriots culture to the other teams, but they did not have the history or the early, quick results to make it stick with a new set of players and a new front office.