I really doubt it. And remember, Lincoln could have cared less about the slaves, so that is not even an issue in this discussion.
I think that Lincoln's expenditure of effort on behalf of the 13th Amendment showed how much he cared. But regardless of Lincoln's attitude many southerners, with good reason in my opinion, saw the CSA as government of the slaveowners, by the slaveowners, for the slaveowners in which the servitude of the poor white slaves only differed in degree from that suffered by the black slaves.