In “Evidence”, Asimov is markedly careful not to reveal whether Byerley is a robot, and not to leave any evidence one way or another. This story is constructed very much like a mystery. We have clues, but no telling clue, no protagonist to expose the plot at the end. Or do we? Susan Calvin is very much Asimov's heroine, so by mystery conventions her word is the author's word. When asked whether Byerley was a robot, her reply is
Oh, there's no way of every finding out. I think he was. But then, […] what difference would it make?
So there you have it: it is very likely that Byerley was a robot, but that is not the point of the story. Underneath the mystery wrapped up in science fiction, this is a story with a moral — that it does not matter whether Byerley was a robot.
I disagree that “The Evitable Conflict” shows Byerley as misunderstanding robots. He has an imperfect understanding of them. He's not an expert robopsychologist, any more than most humans are expert psychologists. Susan Calvin is an expert, and so she can understand the Machines better than Byerley.
The Machines apply what Asimov would later call the Zeroth Law. In Susan Calvin's words in “The Evitable Conflict”:
No Machine may harm humanity; or, through inaction, allow humanity to come to harm.
In “The Evitable Conflict”, this is not an extra law but rather the Machines' perception of the First Law. Unlike most robots, which normally interact with individual humans, the Machines handle humanity as a whole, and so their First Law potential is determined not by the sum of the harm they are causing to a few individual humans but rather by the sum of the harm they are causing to all of humans. Furthermore their experience is removed from individual humans, and robot's perceptions of humans is very much like empathy, so individual harm is something they see from afar and give little account to. These effects are manifest to Susan Calvin, but if Byerley is a robot, they would be alien, verging on inconceivable to him.
By the way, if you read “Evidence” carefully, you'll notice that Byerley, like the author, is quite careful in avoiding directly stating that he is not a robot. He'll express surprise or scorn at the idea, declare that he is legally a human, deny that he can be proven a robot — but he doesn't outright say “I am not a robot”. While Asimovian robots are certainly capable of lying, this is not their normal behavior, and Byerley, if he is a robot, is no exception. The Machines, on the other hand, thanks to their distanciation from individual humans, have no compunction against lying to one. This is another hurdle for robot-Byerley's understanding of the Machines.
If I remember correctly, Byerley's roboticity is alluded to at some point in the Robots and Empire series. All that tells is that history will remember him as a (probable) robot. Oddly enough, Robots and Empire makes the best argument against Byerley's being a robot: R. Daneel Olivaw is officially the first humaniform robot, and his design and construction was quite a feat, so it is surprising that another humaniform robot, about as sophisticated, would have been constructed centuries earlier. The Caves of Steel, which introduces R. Daneel Olivaw, was published in 1954, 8 years after “Evidence”; so this minor discrepancy is excusable. It is also minimized by the fact that Byerley was an isolated case designed by a lone genius inventor (a role that Asimov put much store in, quite strangely for a scientist).
I don't believe Asimov ever explicitly said whether Byerley is a robot. I think he would fully agree with Susan Calvin's words above.