Applescript to get MS Word current word count?
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).