Is there an AppleScript command which will grab the word count of the currently open Microsoft Word® document?
Yes. You could use this:
tell application "Microsoft Word" set theDoc to document 1 return document property "Number of words" of theDoc end tell
Since you asked for the word count of "the currently open Microsoft Word® document" this does it. This script works ONLY in the case where you have a single Word document open.
It works for Word 2011 and for Word 16.25 (from Office 365).