If you mean "batch" and not "draft", then your DAT should be complete by the 3rd week of May, and maybe you could push it one more week. But it would be extremely tough to take it in the month of June and still be in the first batch, unless you sent the application out without DAT scores, and I just can't recommend that. My opinion is that you basically one chance for a solid review by a school, so why would you want them looking at your application, only to discover that it was incomplete, so they put it in another pile and then you're reliant upon them ever going back to it. Make sense? Best of luck to you.