I have the same GPA as you and a 24AA (no section below 20) and as of right now Im laying in the corner of the ring half dead. 2 pre-dec interviews, one is a rejection the other is waitlist and 1 post-dec interview in January. Im probably done for this cycle.
Want a better fighting chance than I had? Do research and community service (as well as scoring well on DAT).
It's important for you to understand that low GPA applicants have a considerably lower chance at most schools. Like, <20% of those admitted overall. There is a general wisdom that one can boost the other, but what really needs to happen is your entire app must be raised to a high level. You have to be well above average in every other way to compensate, not just with DAT scores.
I had a 3.4GPA with a 25AA. I've been very successful with some schools (e.g. my state school, Nebraska (which is very hard for OOS), Columbia, etc.) and have not heard a peep from other schools that I thought valued DAT higher than GPA (e.g. Louisville, Tufts, etc.) so it is so random. I'm also a non-traditional and have a ton of ECs, so I'm willing to bet that some schools value that more than others. Bottom line: you will definitely have a good shot with your 3.2 and a higher DAT, but also try to be as strong as possible in all other areas of your application and apply broadly!
I do think that they can help balance each other out, but make sure the other parts or your application are in shape--shadowing hours, ECs, etc. You're going to need to be well-rounded.
However, I'm going to be sort of blunt here. It is really, really hard to get a 24 on the DAT. You can prepare all you want, but once you get into score ranges that high, I think luck plays into it a little bit. Maybe you'll get a test that plays to your strengths, or maybe you won't. Regardless of how smart you are, I wouldn't bank on a score like this. If it happens, fantastic!! But, if not, it isn't surprising. I think even a 22 would be a more realistic goal, and even that would be above average.