I am a self-taught programmer and I do not have imposter syndrome. I have a degree in electrical engineering and when I thought that was going to be my career I did have imposter syndrome, so I'm not immune. I wonder if there's a correlation. It seems that many if not most professionals suffer from imposter syndrome; I wonder if that's related to the way they learned.
When I say self-taught, I don't mean I never took a class, I mean the majority of my programming skill was learned by doing/outside of classes. I took a Java class in high school that helped me graduate from procedural languages to OOP, and I took classes in college but with few exceptions the ones that were practical (vs theoretical) covered material I already knew.
I've found that imposter syndrome generally comes from misinformation. Once you start talking to peers and understand that they also go through the same steps you do, you start understanding that you belong.