There is proof in the Secret Ansem Reports. He said there was darkness in people's hearts, and in order to protect Radiant Garden, he needed to experiment on it. And Xehanort, his apprentice, had volunteered. So this was written after BBS, when he could have easily witnessed those events and came to that conclusion.
The thing that irks me the most about saying AtW knew about it is that why hasn't he ever consider it then? I mean, ok, he might've known about the Unbirths, but it's also been shown that he
stopped his research halfway. Ansem the Wise never really reached any conclusive evidence nor proof or conclusions in fact, because Mickey came and told him "stop, don't do it, it's too dangerous".
So even if he knew about Unbirths, I doubt he knew anything beyond that there were creatures born from the Darkness of the Heart. He later on only had Xehanort's research and creations to base on, and seeing how by then Unbirths were no longer around (to be found, not necesarilly extinct) then neither Xehanort's nor Ansem's researches could've been about Unbirths.
Xehanort's researches were what made the Nobodies and Heartless; the Unbirths were left as mysterious, unexplored and unexperimented on.
Knowing about Unbirths hardly means Ansem the Wise knew what they were to a level he could explain Namine as such, and I provided enough quotes to show that no, he didn't really have enough evidence to base Namine being a
Nobody on.
He knew there were three things -
Somebody
Heartless
Nobody
???
Seeing how Kairi would be either the Somebody or the Heartless/Heart, that left Namine, the by-product to be only the third option without him ever truly considering the fourth option since he never truly know about it.
The more I think about this the more it makes sense.
If the Unbirths were truly the reason why AtW began studying the Heart, it would make the most sense he'd know the
least about them aside than "there are creatures born from people and Darkness" - but that definition applies nicely enough to Heartless and Nobodies. By the time any true progress was made with the research, Ansem himself had long since stopped it, and then Xehanort made sure that Unbirths would not be what came out of that process but Heartless.