No, that feature has been removed from the game.
Well, actually it's never been in a Halo game the way you describe it. In previous Halo games, switching the language of your console would switch the game's language too.
And by game's language, i mean the texts and the voice of the multiplayer announcer. The voices in campaign always stayed the same.
Example: I'm german, i have my console's language set to english but in Reach the campaign and firefight voices were in german anyways. With english subtitles.
I do hope they add a similiar feature to Halo 4 at some point.