Most certainly, children learn to speak the language of their peers, whether it's English or the lingo of the latest TV show. Experts agree that children of foreign-born immigrants typically learn fluent English from the outside world, even if they never hear it at home. They start picking it up as soon as they get out of the house, and generally master it by third grade, without an accent. Indeed, English often becomes their permanent, primary language. To do that, they need to pick up the customs and language of their peer group.
Children are extremely motivated to communicate with other kids who are in their social group.
The language learned may not always be proper English, of course. It's whatever vocabulary is needed to be part of the social scene. We're pretty strict about what our children watch on television, but they also know all about Spiderman and the Power Rangers because it's what their group talks about. She certainly didn't learn it from us. But most important, kids learn social skills from each other.