Yes and no. What makes a good team is a lot of parts working together well- a coaching team (don't ignore the other coaches!) with a good game plan, a leadership core, good defence, depth to last the distance and be able to respond to what other teams are doing, and lastly a winning culture. These all work together and being hyper fixated on any one to the detriment of the others will only be a short term salve. It's the good GMs who manage to keep an eye on the big picture and understand how changing individual parts influence the whole.
So a coach can walk into a team that has been under utilised for various reasons, or work with the GM to work out where things need to change, but of course as you said, they're not miracle workers. I don't think even the best coach in the world could have coached the sharks into the play-offs this season considering their ageing core, to give an example. A good coach is an important part of the mix, but one that still needs to work with the other parts.