I had ZERO research and got into Western. Do people get into state California schools without research? I am quite sure the answer is probably "yes." Can you get in without research? TBD. I think the answer to this question is another question: do you enjoy research? If so, pursue it. If not, solidify the rest of application...nail your PS, round out your life experiences, and do well on the DAT.
If you are on the fence of "should I spend the time to do this to make myself look good" you could always try research to see if you enjoy the process. I am sure you could coordinate a shadow experience with some researchers at your university.
Best of luck!