Only if people let them. Violence is a harsh reality of the world we live in, but contrary to what is popular belief (because pastors and politicians keep fearmongering to us) studies show that youth who play violent video games are less likely to commit violent acts. Now this doesn't mean I'll let my child play Grand Theft Auto or watch Kill Bill vol. 2 when he's 3, or 8. But if a child is raised in a home where he understands responsibility, the difference between reality and fiction, and understands what is appropriate behavior along social norms, then violent movies and games can be an outlet for teenagers.
It's also important to talk to a child when a violent scene is on the TV or in a movie. An example is during "The Lion King" to ask how he feels after the scene where Scar kills Mufasa, if he understands why he feels that way, and if he knows that what Scar did was wrong and why.
Violence on T.V and Videogames is almost unavoidable, so it all depends on his/her parents, teachers, pastors, councillors and role models on whether s/he becomes desensitized or not.