Watch it at Amazon
Most likely no. However, keep in mind that this movie could be a couple of years in the future, so they perhaps created the materials needed for the ship to stay intact in the hot temperatures in the Earth's core. Also, the deepest any human has gone is seven miles (not past the crust) and it would take a monumental effort, if not impossible to get any further. Also, keep in mind this is a science-fiction and that anything can happen.
Not very realistic at all. You can find more detail information about the physics from this review of the move (made by the Intuitor): http://www.intuitor.com/moviephysics/core.html
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