He may have outrun it, but he never escaped it. It was just too much a part of who is began as, who he achieved some fame with, and who he died as. It's a tragic truth that in his lifetime race was a virtually indelible stamp on society. He ran, as pointed out above, but he could not hide--or escape--the spectre of racism.
There is no question that the prejudices that one encounters in one's youth make an indelible mark upon a person. Therefore, because of his Jim Crow childhood, and the stultifying home environment in which religious and social conformity are demanded, the very individualistic Richard Wright developed a somewhat inverted perspective in which he became suspicious of members of all races. This negative perspective made him openly critical of writers of the Harlem Renaissance, and other contemporary writers such as Toni Morrison. Wright declared,
Negro writers have been far better to others than they have been to themselves. And the mere recognition of this places the whole question of Negro writing in a new light and raises a doubt as to the validity of its present direction.
Wright felt that the potential for social change was squandered by this failure of the contemporary black writers to seek to link the future of the black masses to their own. He perceived these writers as damaged by the attitudes of the past which he, too, seems to never have completely escaped.
It might be said that it is impossible to "escape" racism so long as there are people with racist attitudes. So it would be better to ask whether Richard Wright was able to overcome the racism that plagued him. Since Black Boy is his autobiography, you can pretty much say that, yes, he did overcome. As the eNotes study guide says, Black Boy is "a powerful story of the individual struggle for the freedom of expression." He published several successful novels and was awarded the O. Henry Memorial Award for one of his short stories.
Regardless of his success as a writer, his upbringing in the Jim Crow South forever made him distrust white people. Fearing questioning for having been briefly involved with the Communist Party, he left the United States and never returned.