Generative Grammar is not a foundational work for NLP (natural language processing). Some recent work in machine translation is using more information about syntax but even that has a rather tenuous connection to Chomsky's work. There are some strands of work in NLP that have some connection but the above is a huge exaggeration.
The Chomsky hierarchy however is still taught in undergraduate computer science courses on Theory of Computation, and probably always will be.
Seth