At a 12,000 foot altitude? On that utterly barren mountain?
I dunno. Sounds like an unlikely place to build a monastery, even if you wanted a remote location. The top of Mt. Ararat might as well be Mars.
I'd like to see some detailed drawings/photos of the layout of that structure to get a better sense of what it might have been.
http://health.howstuffworks.com/tibet-altitude-sickness.htm
Average settlement altitude in Tibet: 16,000 ft.
Facts are utterly stubborn things.