Coaching makes a difference in player development. If you hire low end coaches at every level of the minors your players will not develop to their full potential. Also, young players may add 1-3 more points to ratings while in the majors if they have very good coaches in the majors.
It is said that good coaches at the major league level help slow down the decline of older players. How much slower nobody really knows for sure as the makeup rating plays a role in decline as well. As for outcomes of individual games, most think coaches have very little to do with that.
Coach hiring has always been one of the least favorite aspects of this game. However, if you just go minimum $$$$ on coaches all the time it makes having a successful franchise long term more difficult.