IOTL it seems Austria tried to play it soft with Napoleon in 1813/14, giving him again and again a Chance to get out of the war with his throne intact. Yes, Balance of Power played a role but also that on day a half-Habsburger could sit on the throne of France. Without that, Austria may join the alliance earlier and may be more determint to destroy Napoleon. Maybe so Napoleopn doesn´t get out of Germany after Leipzig.
This is a good point. The Austrians were willing to give Napoleon a deal after Leipzig because of Marie Louise and her son (he refused), they were also the only ones willing to have a regency for Napoleon II. Even during the Hundred Days, Napoleon was willing to like to France (which he did till the end) saying that Austria was on his side for the King of Rome's sake and Marie Louise was coming at any time. With no Austrian alliance he can't do that.
If Bonaparte's heir is just some jumped up heir of lower nobility along the lines of the Murats and Joseph's daughters its hard to see anyone willing to fight for his family's right to anything (in fact it is much more likely the allies would be even more harsh on the family). Outside of Napoleon's allies (Saxony and Bavaria, Polish noblilty) it's hard to see any traditional royal house marrying his son - especially if said son is still a child when Napoleon is toppled (which is almost a certainty if certain things - like Spain and Russia - turn out the same).
And while it's almost a certainty that Napoleon III (who was actually a good politician and manipulator even not the military genius his uncle was) would not rise to power if a legitimate Napoleon II was still living and not an Austrian, who knows if the kid will turn out to be as likeable and capable as Eugene, just because he is Josephine's kid.