If by mediocre you mean average and bland, and not of a high quality, then yeah, I'm happy to play through some games simply for the story. I've played games with far too much of a turn based influence simply for the story.
I still play Oblivion, for the story.
I bought Homefront, largely for the story.
However, poor gameplay doesn't really work so well for me, if a game has poor gameplay in such a way that they cease to be enjoyable to play, it is irredeemable. No-one should buy it. It should be forgotten. If I wanted only story, I would have read a book. Or better yet, the Wiki Synopsis.
The reverse also applies: I've almost quit several games in disgust due to their offensively poor stories (Call of Duty: Black Ops, BattleField: Bad Company 2, Lost Planet: Extreme Condition (This one was mainly because of the way the story was told, simply put, I cared not for the characters, and on the flipside, the gameplay was irritating and the few brilliant points of sparkling innovation were outnumbered by the crass crap elsewhere.))
I have a philosophy on Game stories: If your game does not do story well, or if your story is not coherent and makes the game WORSE, then don't use it. Better yet, use a minimalist story.
Left 4 Dead and Portal both demonstrate that by being minimalist with your story, you can avoid plot holes and boring the player, whilst making their experience much more entertaining.
TLDR: Games with stories have the responsibility to tell good ones that do not make the game worse. Gameplay and poor stories both are capable of ruining a game, even if the other is fine.
And I'll play through bland RPG's and FPS's for the story.