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Given a choice, I'd personally do the job in Word if it needs to end up in Word. Acrobat is pretty good at exporting to formats Word can read, but it's never been perfect, in my experience, so there's always some additional time needed to tweak the Word file when I'm done.
I agree with Peter...do it directly in Word. One benefit is that you will become more versed in using Word in the future.
That said, export an existing publication from ID to PDF and use Acrobat to export to Word. With each Acrobat version the Word export has gotten a lot better. There will still be work in Word, like lerhaps moving graphics to headers, making sure styles are set up correctly, etc.
I agree with Peter. Depending on the nature of the document(s), your proposed InDesign > PDF > Word workflow could indeed cost you time rather than save it. A word processor just doesn't support the same levels of typographical detail that InDesign does, and Microsoft apps don't handle even features that appear common the same way that Adobe apps do, so by not working in the native Word environment, you're complicating the results; not simplifying the task. Word will feel just as quirky after you convert, and getting it all right will amount to rework, whereas you could have just done it once.