it's not too late to apply, but you've painted yourself into a small corner in terms of choices. you probably will get accepted somewhere (if your DAT and GPA are outstanding) but it probably won't be your first choice. if you haven't even started studying for the DAT, then it is too late.
you also have to remember that the application process is very expensive, time-consuming, and you should only apply when you are ready and think "yes, i'm definitely going to be in the entering class 2006." if you apply this year and don't get in--and then reapply next year--you'll have to find ways to improve your resume in those few months (because schools/interviewers will ask you "so, what have you changed since the last time you applied?).
IMO, if you aren't ready for the DATs, save yourself a lot of headache and money, spend the next few months studying for the DATs AND shadowing, and then apply in another 7 months (mid-May, when the application comes out).