“[Jefferson] Davis will not be found guilty and we shall stand there completely beaten.” — Judge Francis Lieber
Given the spirit of retribution which took command of the country after Lincoln's assassination, the acquittal of Jefferson Davis was still far from certain, but the trial itself would have been a huge embarrassment for the prosecution regardless of the outcome.
From a legal point of view, I am not sure the issue of succession was ever settled. However, the ham-handed manner in which it was handled in several southern state legislatures did not follow constitutional muster either-- it was basically rammed through with little or no debate and over the objections of a significant portion of the state's citizenry.