Yes, Martin Luther King Jr. believed that change would have come gradually overtime without the non-violent protests he was leading in Birmingham.
In his "Letter from Birmingham Jail," he wrote that "the ultimate tragedy of the modern world is not the triumph of evil, but the triumph of non-doing; the incapacity to act together as human beings in the face of common danger."
He believed that the only way to bring about lasting and meaningful change was through direct action, which would force people to confront the injustices of segregation and inequality.
So, King's belief that change would have come gradually overtime without non-violent protests is consistent with his philosophy of nonviolent resistance.