Others have brought it up, but let's recall that Zelda sang the latest LoZ game, Skyward Sword.
[video=youtube;nscxtnwu11E]http://www.youtube.com/watch?v=nscxtnwu11E[/video]
However, she only sang in Japanese, which obviously most of us couldn't understand. I liked how it sounded on its own and thought it fit that certain scene quite well. The problem I foresee with this is making it sound Zelda-ish all the way through. I'd honestly be fine with Japanese lyrics/vocals, but English would fit the atmosphere better for me if they used it throughout a game.
Another issue, of course, would be the lyrics. Players who prefer the adventuresome tracks of Zelda won't be for it, unless the words helped to maintain that adventuresome feel. The lyrics might sound cheesy in many gaming instances. Now, the video below is a sample about what I'm discussing. In my opinion, it'd need to be sharpened up to be used in-game (not suggesting it's bad; it's quite marvelous, actually), but I could see something like this style.
[video=youtube;LGXIY8FgWSI]http://www.youtube.com/watch?v=7FjZ4Djghkw&feature=iv&annotation_id=annotation_757692[/video]