I don't have Word 2011 (or any other Windows app), but I do have Pages and just tried it - and here is what I got:
Open blank doc in Pages, turn on "allow to write in any app" in Ink Preferences, got a "scratch pad" and scribbled a couple of letters, scratch disappeared and the letters showed up as "typed" in blank document. Scribbled circles did not, only letters - so, it appears it recognizes it for writing, but not drawing.
I then used the Ink pad to draw a smiley face and, according to the Ink Help, you can "send" it into the active application, but Pages would not recognize my drawing, which - in a way - does not really surprise me because Pages is a word processing app, not a graphics/drawing app.
I then tried the same thing in the old AppleWorks (with a blank drawing doc open) - drew a smiley face, hit send, and it showed up as a smiley face!