Well, I neither know a blind programmer, nor do I know much about it. At least, I read an article (German), which states that they use TTS programs which read the code and add additional information at a very very high speed so that they always know where they are in the source code and can get a hint what the surrounding code does; just like we can read the code, they get it read for them and then decide on it.
Blind people are amazing. They cannot see, but all their other senses are elevated instead, so they can do stuff like listen to that fast blabbering and make sense of it.