Is someone who is born abroad to an American citizen an American citizen since birth? Would he/she be just as American as someone like me, born in the States?

Lee Child explored this idea in his Jack Reacher stories.

Reacher was the child of a serviceman, spent his entire life on various bases before growing up and becoming an officer himself. So most of his first 40 years was spent outside the US. He was as American as if he'd been born and raised in the States but he sometimes felt like a stranger in a country he didn't know physically.

I am a US citizen, but I was born, and have lived all my life, in Australia.  I've only been to America 3 times, each time in June/July and for about a month each.  I am also an Australian citizen.  I consider myself both American and Australian, but when someone asks me if I had to choose between the two, I say Australia because it's where I've grown up, and I've learned Australian values and live an Australian way of life.  When I go to America, I am out of place, even though I am a citizen.  I speak differently, and I know different things.  I couldn't tell you the first thing about how American politics, but I could give you a detailed run through of the different levels of government in Australia.  I also speak differently.  I say coriander instead of cilantro, aluminium instead of aluminum, thongs instead of flip flops.  However, I think that I have a more realistic view of America and American culture than other people I know because I've grown up hearing about it from family, and I know intimately, and have met, a lot of people who live in America.

So, an American citizen born and living overseas is an American, but in a different way to someone who has lived in America their whole life.