Um no; if you climb the everest, or at least pretty high, you won't die because of the lack of pressure (though you might find it difficult to breathe).
Your hard drive however will die : The hard drive head requires an "air cushion" to hover above the disk, if the air pressure gets too low, the head will go down and scratch against the disk, damaging it.
A computer with a SSD instead of a HD shouldn't have any problems.
Is anybody seriously thinking about bringing a MBP up Everest?