The answer is maybe. GameStop usually does do repairs, but it doesn't mean that they can/will fix your game system. I've actually heard that they're unreliable (i.e. lengthy service time, failure to fix anything, even lost items).
I recommend going with Nintendo. Like was said, it will probably be free if the warranty is still active (though shipping fees are likely to apply), and you may even receive another year added on free.
(Try not to bump threads if you have little of value to say.)