Well, yes and no. I write everything either in LaTeX or markdown these days, but its ridiculously simple to output either of these formats to docx, so normally that's what I do. I'll always send them the PDF version of my resume first though, as good typography can make you look better.

If a job requires me to write in Word throughout the day, that's a job I don't want (in fact, writing grant proposals in Word was one of the most frustrating things about working in adeademia).