What would people drilling through Mount Everest find?
The summit of the mountain is made up of 400 million year old sedimentary rocks laid down long before the uplift 50 million years ago.  These rocks contain marine fossils including Trilobites and Crinoids. If you drilled down from the summit you would then encounter older metamorphic rocks,  the upper parts of which contain traces of fossils, and then in to gneisses and granites.
http://all-geo.org/metageologist/2012/06/the-geology-of-mount-everest/