Mount Everest volcano
Mt. Everest was formed (is forming) by two tectonic plates colliding-the Indo-Australian Plate and the Eurasian plate.
Sometimes, when two tectonic plates collide, volcanoes form (such as the Juan de Fuca plate and the North American Plate forming the Cascades). However, this has to do with one plate-in this case the Juan de Fuca Plate sliding or subducting beneath another-the North American Plate. This happens because the oceanic plate (the Juan de Fuca Plate) is more dense than than the continental plate (the NA Plate). For reasons I won't get into here, magma forms between the two plates as one subducts beneath the other and volcanoes are formed.
Mt. Everest is formed by two continental plates colliding. Continental plates are generally too buoyant to subduct beneath each other. While some subduction occurred during this collision, most of what happened was crustal shortening. Think about what happens when you have a rug on a wood floor and push two ends toward each other. It buckles and folds up in itself. This is a simplified version of what happened in the Himalaya.
Because little to no subduction is occurring, no magma is forming and Mt. Everest will not become a volcano.
Additionally-mountains don't "become" volcanoes. Volcanoes form mountains.
Note: this is an oversimplified answer and I would suggest researching further to get more in-depth information. All information for this answer came from the many geology classes I have taken and taught-I don't have anything to cite at the moment.