Quote from DarkBlade

Quote from HatakeKakashi

Quote from Dr. Love

Like loose, I retain my scepticism. Also chakra depletion doesn't mean you're dead. Chakra is basically stamina. When you run out of stamina, that doesn't mean you die. Or else Sasuke would've died as well (Deidara fight).

really?

I thought Kakashi mentioned something about when you run out of chakra you die...

He said exactly:"With my current ammount of Chakra his whole body is out of question.
And if I use it again, that´ll be the last of my stamina and my Chakra.
...and without a doubt...
I´ll die!"

Agreed. I read that as Kakashi having no stamina or chakra left, so he's helpless and/or will pass out (like he did the other time he used MS and said he would do if he used MS against Kakazu).

As for Naruto not sensing Kakashi's chakra...if he's alive, it would probably be because he has almost none and is passed out and and possibly on the verge of death. Also, Tsunade's lack of a response does mean anything...it could be because he's dead or because he was defeated and injured. Both of those are rational reasons for her reaction and fit with her personality.