I usually associate the term "The Media" with news corporations like CNN and Fox News. So im going to assume thats what you mean. If that is the case, I wholeheartedly say "no". News corporations usually only report on violence, not actually showing it most of the time (except for footage from gas station security tapes and spectator videos of plane crashes, that sort of stuff).
But if you are referring to "media" in the sense of video games, TV Shows and movies, then yes, I completely believe that the things children watch and interact with affect their behavior. That's simple and basic Psychology 101. I remember when I was 8 years old and I got to start playing Call of Duty 2. It significantly altered my behavior in that I was oftentimes pretending I was in the game when in reality I was in average everyday real life, at the grocery store with my mom or playing in the house going "Die, Jerries!" and "MG-42 on the hill! Take cover!". There were several incidents where I actually hit other kids or inappropriately interrupted social situations where adults were talking at a house party or sunday school gathering.
Also consider that children are by far much more easily decieved and influenced than at any other age. History is full of examples of societies where children are indoctrinated from a very young age. North Korea where kindergarten and pre-K kids are taught all about "the great leader", or various corrupt Islamic states in the modern middle-east, where children are trained from a young age from groups like the Taliban and CIA to hate americans and sometimes even be Self Delete bombers.
This goes for the west too. There are a great many children across the south US who are forcibly indoctrinated about Christianity from a young age, but are never actually in a loving relationship with Jesus, but rather just following along in the motonous routine of dead religion in a children's suit/tie or collared shirt on sunday mornings. Those types of kids end up growing up to go into their high school and college science and history classes to finally have the final smack to the glass shatter their lifestyle of empty religion. I'm willing to bet that's the common background story for most of the young adults and teens in my school and area that consider themselves agnostic or atheist.
By no means though am I saying true Christianity is this way. Sadly the majority of "Christians" in the US are nothing more but phonies. They are simply following the robotic and loveless routines established by their super-conservative parents or grandparents. I've seen it before in the churches I used to attend; the Megachurch in downtown Jacksonville. There were hundreds of kids in my sunday school class then but I could only name a handful of people out of that entire group that really had chosen to follow Jesus rather than simply following along in dead religion.
I'm lucky now to be going to a small church that's an extended campus of my former megachurch, and down here, the people actually love one another and care for each other, and they really have a heart for the Lord. It's the best thing in the world to me.