Some people will indeed be influenced by what they see on TV.
Others will not.
There are two novels that can change a bookish fourteen-year old's life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs.... John Rogers
They have been researching this stuff since before the flood. There is some data to show that it does in some cases but for the most part there is very little data that it does. Children will usually act out in play about things they see on TV or movies but I assume the OP is targeting real violent behavior. In that case I said no.
"Those who do not learn from history and condemned to relive it".
"There are those who will debate the necessity of wilderness, I will not, either you know it in your bones or you are very very old". Aldo Leopold - Sand County Almanac
No more than any other form of popular media throughout history.
I think it desensitizes people to violence.
It's an influence to be sure. To what extent is the question. Besides, if TV influences a person enough to be violent, there's probably something already wrong with the person.