I'm signed up to take it, so I guess what I say wouldn't be as accurate as most people but from what I understand, having those extra classes done just makes the learning process a little quicker/easier since you've seen the material before. For example, just because you haven't taken human physio in college yet doesn't mean you can't learn the few main ideas you need to for preparation on the DAT exam. So yes, they do help out, but are they necessary? Absolutely not. The most important process is how you prepare for the test and the effort you put in.
For me, I've taken a lot of upper-division biology classes that are necessary for my major (biology) and going through the list of things I need to learn for the DAT, I'm obviously glad and more at ease since I've seen so many of these topics before. However, there are certain classes like Plant Biology that I would never take as an elective biology course, so I have to learn the basics.
You have basic biology and general chemistry down and some organic chemistry, I would personally say go for it if you're certain as a sophomore that this is your path!