In reality, the question was not union or disunion. The question was whether to keep their federal system or replace it with the consolidated national system of the new Constitution.
We of course know this was very possible - we have the examples of the United States of Central America, the Grand Columbian Republic, and the Peru-Bolivian Confederation, all of which broke up into component parts shortly after they achieved independence. Mexico underwent a similar breakup during the 19th Century, with some of the components eventually reuniting with Mexico (Republic of Yucatan, Republic of the Rio Grande), and others winding up part of Mexico's neighbor to the north (Texas, California).
My opinion is that the Constitution was the last chance before permanent disunion. There's nothing inevitable about one large republic between Canada and Mexico, to my knowledge no republic had ever existed on that scale (The Roman Republic was not - it was a city-state with an empire grafted onto it - and eventually the empire corrupted the Republic.) Breaking up into a bunch of perpetually squabbling independent states was probably the most likely outcome, and it is part of American Exceptionalism that it did not happen.
The Antifederalists may not have wanted disunion and perpetual turmoil and war, but if they had succeeded in blocking the ratification of the Constitution that is probably what they would have gotten.