I guess he could technically be alive, since he's such an important chacracter. If so, then the Night's Watch is full of incompetent assholes if they couldn't even manage to finish off a dying man with multiple stab wounds.
I'd bet my bottom dollar that he's alive, or at least, that he's not "ned dead." Sadly in these books, you can say that a character is "Dead" and they're still "Alive," so, my meaning is "ned dead."
Top theories [of mine, and others]:
1) Jon is stabbed something serious but ol' Melisandre and her black magic raise him up, Azor Ahai and all that stuff.
2) Jon was stabbed someething wicked but enough not to kill him *on purpose* by his friends up at the watch, knowing that it was the only thing that could keep him at the Wall; he'd flee south otherwise, so they mame him as best they can to keep him there.
Frankly, I could just be naive, but it would be just a horrific waste of time if Jon were truly killed off at this point. Just... ridiculous and it would convince me that GRRM got mad that readers figured out the story before he could tell it, so he twisted it into some bull shit to throw people off.
But, I don't for a moment believe JOn is actually dead. Either Jon Zombie (which I would be disappointed by, sick of zombies in this book; kind of wnt dead people to stay dead), or not zombie not dead.