I had Black Mollies and they did, indeed, eat BBA. I had to keep them hungry, though (only fed fish food twice a week, and in moderation). I could certainly believe that the Balloon Mollies would eat BBA as well.
I picked up 3 balloon mollies today, 20 min after introducing them to the tank, i see them eating the BBA. I also grabbed 3 black mollies and they are also eating the BBA. They seem to be getting along pretty well too.