Being of the RPG vein you might think that I would be inclined to say "YES.. everything else is irrelevant" but I know that simply is not true.
A game such as Demon's souls shows how even in a story driven realm like RPGs, that a story can easily be trumped if the gameplay is good.
HOWEVER.... I do think its very important and far too often game, typically of the shooter mold have this misconception that they can get away with making the narrative an afterthought because "who plays shooters for anything other than multiplayer amirite?"
I think people are starting to realize that notion is becoming antiquated because of how we are now starting to see the emergence of multiplayer and story elements being intertwined.
So technical answer, no. But rule of thumb that game developers need to follow at all times, is yes. Because really, crafting a decent narrative is not really that hard and if nothing else, you can use it as a fallback position, because in many cases people will overlook some bad gameplay IF the story is good. I dont think the same can be said for the inverse. Sure pure fans wont care either way, but the fringes of your market will likely be dissuaded.