Pretty much.Damn, hadn't throught of that, So Napoleon III could, realizing this, offer his service to his cousin?
While it might be "too late" to do anything about Louis Napoléon's I misspoke in my above post, both boys were "Louis Napoléon" and "Napoléon Louis") marriage to Joseph's daughter, a lack of service in the Carbonari would definitely butterfly away his death from measles OTL and it MIGHT mean he and his wife spend more time together, hence having kids.
IDK why but I'm imagining Reichstadt either arranging a marriage for his cousin (Mathilde) to a minor (but rich) Austrian archduke or at least a prince in Austrian service. Not because he feels indebted to her, but as part of broadening his "alliance" network. The second son of Karl, duke of Teschen, was certainly well off enough (albeit small fry compared to his older brother who got the bulk of the inheritance). Other wealthy archdukes include Stephan of Hungary (once his dad dies, and since his stepmom hated him, and Mathilde's stepmom's cousin, it would be a wonderful way of screwing with the Dowager Palatine, especially since Stephan's match to Olga Nikolaïevna was Metternich's project), Maximilian d'Este (brother of Francesco IV and heir of his late uncle and namesake, Maximilian, Elector of Cologne) and Ferdinand Karl d'Este (although I think that was due to his Hungarian wife). Princes in Austrian service include Ferdinand of Koháry (OTL King of Portugal, personally think he and Mathilde will get on splendidly with their shared artistic interests), the Nassau-Weilburgs (Frankie's former regimental commanders), several minor princes of Württemberg, and some Hessian boys (ICR which ones).
Another "fun" fact is that Reichstadt may help Gustaf V get an annulment from Luise of Baden. Or at least, get grandpa to put enough force behind Gustaf so Gus can marry Marianne of the Netherlands (and get a happier marriage for all involved). Why does Frankie do this? Gus is the guy in charge of Frankie's first army regiment. And Gus liked/was impressed by Frankie, so call it a favour for a friend.
Back to the Bonapartes, Frankie would likely arrange one or two other marriages there as well. This isn't because he likes them, but I suspect Europe is going to be shuddering at the prospect of him marrying, so he'd have to "secure" the succession by other means. First on the roster is likely OTL Napoléon III if his brother has no kids by the time Frankie really gets a head of steam in Austria in the late 1830s/early 1840s. Likeliest candidate? Princess Alexandrine of Bavaria. OTL she was considered for Joseph Bonaparte's eldest grandson, and given Frankie's OTL friendship with here mom and dad, I could see Ludwig I having fewer excuses about why she can't marry. Mathilde's brother might be easier to get an "actual" match for that isn't family. Mostly because his uncle, Wilhelm I of Württemberg, liked him enough. Certainly more than his own son, according to Olga Nikolaïevna's memoirs, so that would probably help him find a bride. OTL Plon-Plon will be so unimportant here that it'll be a miracle if he weds at all. And him not marrying will be no bad thing IMO