Well, in my opinion (which is semi-biased, mind you), I believe Napoleon could actually keep his throne in the Hundred Days. If tensions had boiled over during the Congress of Vienna between Prussia/Russia and Austria/Britain over Saxony and some other issues, I believe the Coalition could be split and or hampered. I do not think it would fall apart, but there might be some rough feelings. (Imagine if Prussia decided to sit out the Waterloo Campaign.)
That being said, there could also be the problem of the other monarchs seeing Russia's ability to police Eastern and central Europe as threatening...
In the long-run though, I do not think Napoleon would consolidate and then wage a political and diplomatic campaign to keep his throne. Yes he was physically and mentally reduced and probably wearier of war than at any point in his career, but he was still the man who had defeated all of Europe. He would not sit idly by- I do not think he actually could stop himself from fighting. Maintaining his throne would be difficult without military victories even though he was a dictator from the left. I think after the Russian Campaign, his best shot would be to abdicate for his son, and allow regency for a diplomatically talented individual like Talleyrand to try and soothe Europe. Napoleon would always be a pariah among the crown heads of Europe: When the Coalition armed itself to bring Napoleon down for the final time they declared war on Napoleon, and not France; symbolically to show how they did not want to isolate the French people, and to show that Napoleon was their only goal. (I believe that is the only time countries have legitimately declared war on a single person?...)
Anyway, I think Napoleon may have had a tiny chance to retain his throne during the Hundred Days. Tiny. But hey, there’s always a shot…