Heck ya have the LORs sent! I even recommend having the LORs sent BEFORE filling out AADSAS, if possible. Typically the LORs are what hold up applications.
Schools don't care what they receive first. Once they receive something from the application cycle, they'll create a folder for you. It doesn't matter if that is a check, a photo, AADSAS application, DAT scores, or LORs.
Secondly, did you have schools marked to receive your DAT scores when you took the exam? If so, those scores should have already been sent to the schools you had marked. If you want different or additional schools to receive those scores, then you'll have to add the schools in order to have official DAT scores sent.
Did this make sense?