Answer
Yes, if we can treat the Earth's mantle as a "liquid" that flows, over geologic time scales.
Work Step by Step
Mountains are similar to icebergs, and extend deeper into the medium they float on than they protrude above it.
See "Floating mountains", page 254. The concept of floating mountains has a name in the geosciences: isostasy. Interestingly enough, the Himalayan mountains mentioned in the question are in an area that is NOT believed to be in isostatic equilibrium (source: Wikipedia entry, "isostasy", 29 Jan 2016).
