Well I have two questions back in response to your question.
1) The original 13th Amendment slated for ratification and ratified by Illinois (seems there was a certain man that came from that state that had just been elected President too) in 1861 stated
ARTICLE THIRTEEN, No amendment shall be made to the Constitution which will authorize or give to Congress the power to abolish or interfere, within any State, with the domestic institutions thereof, including that of persons held to labor or service by the laws of said State
If this Amendment would have finished passage would it have staved off war?
2) Would the northern states have rescinded their existing Black Codes that, again, existed before the War? Illinois was known to have one of the most stringent and Oregon even banned the settlement by blacks in their 1859 Constitution?
Considering the northern states didn't even accept the precepts of the latter day 13th and 14th Amendments before the War, why should you expect the Southern states to do so?