Yes, absolutely it is possible during post-bac with some programs, but that doesn't mean you shouldn't do it during UG as well.
Be choosy with what kind of research though, take the time to look over your profile carefully. Do something you are really interested in and that will enhance your application. I'm a fan of the clinical research projects for pre-meds as you get protocol, research and data experience, but also often work with a patient care team. But, depending on your goals, straight bench research with a productive lab might be better.
So, shop around and ask various programs post bac what they offer or build it into a DIY, you want to find a program and location that has the best opportunities for you and your situation.
Do you have time to do a for credit research project in your undergrad? Are you also working to support yourself? If your GPA is low, be sure you are focused on that improvement first and then balance a research opportunity well with your other courses. I wouldn't want you to stretch yourself too thin just to "check off the research box" on your application and have your grades suffer.