I'm not sure we can construct a complete view of the atonement from Nestorius' works, but it appears he recognized the significance of the passive obedience of Christ in our salvation. Now, whether he would use the "Christ" where he used "God" there, is a more difficult issue (we have so little of his own writings to go on). Given that he called Mary, Christokos, I suspect he'd prefer not to refer the atoning work simply to the name of Christ, but to the person of God the Word.
Please keep in mind that I only used the atonement of Christ as a modern day concern which this controversy influences. I would not import it into those times and make it a criterion of judgment. I don't expect the fathers to speak of atonement in Anselmian categories. By and large they were more concerned with the issue of humiliation-exaltation than with satisfaction.
I am sorry, but I just cannot see anywhere that Nestorius affirmed orthodox Christology. I agree we cannot pin "two persons" on him because we have no statement to that effect; but his language is always in terms of speaking of the Word as a prosopon and the flesh as a prosopon while the "unity" is apparent and moral rather than real and personal. My own opinion is that he was a rationalist who simply could not accept the "mystical union," and therefore struggled to rationally come to terms with how the finite could contain the infinite. We have seen a similar example in Gordon Clark in our own times. I am open to any evidence which suggests otherwise.