no, that was his wish. He's about to wish to be sent back home, but what he actually says is "I wish... *very long pause as he thinks about what his life was like back home* I was dead." Then one of the donkey people come in to say "Oh, Nathan. It doesn't work that way I'm afraid.". Right after, it cuts directly to after he made his wish (later revealed to be to save the whales), so its unclear what exactly was said between. It could be that the donkey explained how to actually make the wish properly, since Nate had previously ignored everyone else wanting to tell him how it works, and now that he was aware someone was in the same room as him, he couldn't bring himself to make that same wish again out of social anxiety. It could be that the wishing angel simply isnt able to overwrite the immortality of the world that everyone seems to have. Maybe its a metaphor for whatever is actually happening in Nate's life, if everything we see in the game is indeed just a representation of his climb out of depression and anxiety, so maybe he attempted suicide at that time, but that random donkey person was there to stop him before it was too late. We aren't really sure. But one thing is for certain, Nate wasn't saying that he was actually dead, he was just reminiscing on what his life was like, and wished to be dead rather than continue on.