No... Midna's made-up language enforced the idea that she is alien to the world of light. Her appearance, her origins, all that is held together by her strange language. To use that for everyone else would detract from Midna's character overall and lessen her appeal and impact.
I think it'd have been better if they made Midna's language a bit more expressive. All the expression was in her body language(anyone else think the mocap for this game has to be some of the best, EVER? Seriously, no one really looks like they're walking stiff or unnaturally). If she had some actual growls when talking about how much she hates the guy, or have the tone lighten up when she's surprised or happy, it would have fleshed her out to an insane amount.
I haven't played the game (but have followed this thread for a while now) - is Midna's gibberish generated in real time (a la Banjo Kazooie), or is it all prerecorded - I mean like someone actually speaking the language into a mic?
It's not a person speaking into a mic, but not really generated in real time either. She doesn't talk as the whole message plays out. It is extremely well done, however.