If you mean by reconciliation an end to the rebellion and the reunification of the country then no, there was no chance. Because the group sent by Davis for these 'negotiations' had as their primary purpose the negotiation of relations between independent countries. In other words, recognize the legitimacy of the southern secession. That was a non-starter from the beginning.
Well, then, we've come full circle.
The Confederacy was illegitimate because the federal gov't chose not to recognize it.... and chose not to recognize it because it was illegitimate.