I would say that, if a system focuses on combat, it will contain combat. It doesn't have to focus on it, but it does have to contain it, or you've wasted most of the system.
I would not argue that it relieves the GM from combat simulation. The GM still has to think through how the enemies would act, and how the current environment would work in the system presented. The presence or absense of combat mechanics does not permit or dissuade focus on narrative elements.
D&D has really limited our ideas of what an RPG can be. If a fight breaks out, you need to roll initiative, right? An adventure will contain combat, so you need a system in place to deal with it, right?
I recently bought a game called Golden Sky Stories where it dedicates only a paragraph to combat. You make an Animal test, then take a reputation penalty for being violent. That's it. You don't need to simulate it any more than you need to simulate cooking.
(Sidenote: Can someone make a cooking-focused RPG? It could be pretty interesting.)