"The Keep will be available to everyone a few months before DAI gets released, in order to give fans plenty of time to experiment with scenarios and make their history exactly how they want." -Mark Darrah
To me this means a full release in August at the latest, as I would consider no less to be "a few months". Now I am sincerely hoping that Bioware/EA isn't planing on a full release without proper stress testing (cough cough battlefield). I really wanted to see an open beta, but I guess if that doesn't happen I wont be to let down. Maybe we'll still get one in July? Asking fans to accept a website as a mandatory component of this game is already a stretch. Fan reactions to the website will set the tone for how the whole game is received.
It is worth noting that Bioware will be at a convention on July 11th that would present a good opportunity to announce a release date for open beta/full release/more details.