My dad's an atheist, and I'm an atheist, so yeah, there are second generation atheists.
It's actually something I used to think about a fair bit. I mean, I was born and raised without any religion, and stayed an atheist by default. It wasn't a struggle, I didn't have to explore my faith or turn away from it. And when I hear stories about some of the things some Christian people went through when they made the transition to atheism, it makes me feel like I had the easy way. On the other hand, I was never not an atheist. And would that make either them or me "more" or "less" of an atheist?
Like in some vampire movies, the ones that are born vampires often hold themselves in higher esteem than the ones who were turned later in life.
Or, to paraphrase Bane in The Dark Knight Rises:
"Ahh, you think atheism is your ally? You merely adopted non-belief. I was born in it. Molded by it."
But that was in my younger days. Since then, I have realized that the only factor defining an atheist is a lack of belief in any god. That's it. How long you've been one or how you came to be one doesn't matter one bit. There's nothing else to follow or do or believe that would have any bearing on how well one is being an atheist.