AppleScript to save active Microsoft Word document IFF there is one
You need to query Word for the count of document objects – active document is just a convenience shortcut to the frontmost one in that list. Unluckily, Word’s somewhat peculiar AppleScript implementation does not return an empty list object when there is no open document, but missing value (AppleScript’s take on nil) instead. Taking that into account, the following function queries Word for open documents:

on hasDocument()
  tell application "Microsoft Word"
    every document is not missing value
  end tell
end


– put that in front of your script and change your conditional to if it is running and my hasDocument() and you should be fine.