Doug you'll also get Analytics with that option set to false. Your Analytics will show all the usual sharing data.
That hash tag is just used for tracking URL copying and pasting, when a visitor doesn't use the addthis services but just copies the URL from their browser.
I've turned that feature off as we use hashes for another reason. What kind of percentage are you seeing for visitors who share the URL in this way, compared to clicking the usual fb, twitter, etc. icons?