I dont think they'll be scoring the writing in June. When you sign up for the LSAT it lists all of the "terms" basically saying what is scored, what isnt. You can sign up for june and it says nothing about having a scored writing section, which leads me to believe that it most likely wont be scored.
I had this same opinion, until I inquired further about when the LSAC disclosed that the June 2005 LSAT would have the additional writing sample. It turned out LSAC made this decision public in mid-march, after many had already signed up for it. So, I dont think having signed up already necessarily means that the writing section wont be scored. That being said, March is basically over, and I doubt they would wait too much later to disclose something as important as that, so the writing section being scored this year is fairly unlikely.