No. The deepest well ever drilled is 7 miles deep. The earth crust is 10 - 40 miles deep. Only nature can cause a eruption like the one in the movie.
Man made drilling while likely not able to make it through the crust before heat and pressure would force the work to stop. Magma pockets could use the weakened areas to push through. Deep sea drilling where the crust is thinner increases the risk.