Not necessarily. Depending on circumstances, it takes a long time with increasingly severe pain/symptoms until eventually the person becomes delirious. One could argue that they probably don't care at that point, but they will have been in pain for a long time before they pass out. K2 is a good book that talks about such an experience.
I'm currently reading this book about various K2 expeditions, written by Ed Viesturs who is a big name in high-altitude climbing. It's really interesting so far! He talks about a few different expeditions, one of which he was on. He also talks about the 2008 disaster, which is probably the most well-known K2 incident.
I was actually thinking of doing a writeup here about that disaster because while we all know who made it down the mountain and who didn't, we don't quite know where everyone was at which time because of conflicting reports.