I am a psycho-and neurolinguist (or trying to be) and, in spite of being interested in it from a theoretical point of view, I have seen a better understanding of language processing and representations applied to education (especially, to learning writing processes), and even to langauge rehabilitation within aphasic population. And the work that is made in a interdisciplinary way (with
neurosciences, physics, and so on) is hopefully based in good and comprehensive linguistic theory. I would believe the same happens with computational linguistics and NLP, and the applications that can be developed in those areas.
So... I guess it does matter!