The vote is canon, only the LC was preserved by a single vote. If things had gone the other way, the timing is actually kind-of amazing. Although the sourcebooks don't go into any proposed details of how the dissolution would have worked, I imagine that some smaller rump states would have cohered and petitioned for Star League memebership, while many other worlds would have simply preferred to existin solely under the aegis of the Star League, with no intermediating "national" layer between them. There could have been as many as several hundred of these worlds.
While I can't see the Camerons being anything but delighted at this news, this severely shakes up the existing order of the Star League. The League, as far as I know, was never framed as anything other than a confederal pact between sovereign states. The emergence of this new class of purely League-governed worlds could have lit fires all over the Inner Sphere. The timing is actually suspiciously great for all sorts of ripples to propagate.
Twenty years later, you've got the Regulan crisis in the Free Worlds, and the Marik's small civil war against the Selaj. This, naturally, quite alarmed the Star League, and garrison SLDF units in the FWL were put on on high alert. The Mariks just managed to convince the Star League that this was an internal matter, so the troops stood down. That mess drove the Captain General so paranoid Parliament tried to "end the emergency" and abolish the position, sparking the Marik Civil War. During that mess it's inconceivable that some worlds - or even whole provinces - wouldn't think of trying the Lyran trick and prying themselves free of Marik's grip.
And just when the Marik turmoil is winding up, with an emboldend Star League feeling its oats and building a power base separate and apart from the Member States, here comes the War of Davion Succession. After the epic collapse of the AFFS in the opening moves of that little spat, I can't imagine that there wouldn't be significant grumbling across the length and breadth of the Suns. The Capellan march is always restive; as late as 2617 New Syrtis was nearly in open revolt. And after the butt-kicking the AFFS just got, the Draconis March isn't feeling too confident in New Avalon's ability to protect them.
All the while, the Star League planets are thriving. As soon as the Reunification War kicks off, investment begins flowing to the Star League worlds that managed to break free of Member State control; they'd be well-placed and secure locations for the SLDF to source parts and build bases, without the logistical problems that come from schlepping everything out from the Hegemony. If the League especially wanted to encourage planets to squirm free of the Member States, they might even relax the Mother doctrine on technology transfer.
So, on the Eve of the Amaris coup the Star League proper isn't just the Hegemony and a handful of jointly-administered worlds. Instead, in addition to the Hegemony there are hundreds of purely-Star League worlds; the majority of the former Lyran Commonwealth, big chunks of the Free Worlds League, and even former parts of the Federated Suns. The only Member States largely intact are the Draconis Combine and the Capellan Confederation.