If the tactical voters know who has voted, they can make at least an educated guess as to which way the results are trending, and vote accordingly. Obviously they would never have the advantage they do now, but they still might be able to eek something out.
I don't think tactical voters would really pay that mcuh attention. I think most tactical voters vote based on either media results (which would be incomplete) or on a vague sense of who's winning coming from the voting both... they won't expend the effort to track down who voted secretly, attempt to make a preference list for that voter, and tabulate the results from there.