We are definitely wired to identify with a certain gender. That's pretty much accepted science, nowadays.
No one has found the slightest evidence that we are wired to identify with a certain race. I don't want to dismiss the idea altogether, but I'm not certainly not ready to conflate race with gender.
As far as Dolezal, and believing that she is African American, consider this:
Supposed I moved down to Mexico. I'd be an American living in Mexico. But suppose I learned Spanish really well, and started participating in all aspects of the Mexican community where I lived. I obeyed Mexican customs and I gave up my American citizenship to be a Mexican.
I'd BE Mexican, right?
The same way someone who comes to America and becomes a citizen is every bit as much an American as someone who was born here.
So I don't see why Dolezal couldn't "become" African American if she wanted to.