When we are exposed to images that are purely meant to entertain, it can dull our sense of empathy. Celebrating people becoming injured or even being over exposed to images of horrific events makes us less likely to be empathic to those events. Overwhelm in this day and age is a major issue for children and adults alike.
I do not believe entertainment works directly against empathy. Empathy is something a person either has or doesn't not have. I think a lot of people struggle with empathy. I think a lack of empathy in the society has led to large problems for the society as a whole, but I don't think that loss can be directly linked to entertainment.
Some of the best forms of entertainment are those that cause us to emote and empathize with the characters in the story. Entertainment helps us empathize by putting someone else's plight right in front of us, forcing us to confront human stories we may otherwise never have considered, and in that way we are more empathetic toward others.
No, entertainment does not work against empathy, because Americans have both. We are not only the most empathetic people on earth, but we also have the best entertainment. America has influenced popular culture far more than anyone else in the world. Even so, we are also the most generous people on earth.