I'm actually in the same position, and applying to almost all the same schools (Columbia, UPenn, Hunter, Fordham, NYU, and Yeshiva.) It seemed to me that many people going into graduate school for an MSW already had a ton of work experience, so I spoke to people from different programs (Yeshiva, Columbia, and Fordham) who all stated that many of their classmates had come straight out of undergrad.
I even spoke to one student at Columbia who told me that oftentimes schools prefer students straight out of undergrad because they haven't been "trained" yet and don't yet have a particular approach to social work.
Now, I can't speak for the validity of her statements, but I sure hope that she was right- if so it would seem like we have an advantage!