However, I think it highly unlikely Quebec would even sign on to OTL Articles of Confederation. They banned the states from having their own military forces, which the Canadiens wouldn't hand over to an Anglo-dominated institution. I also imagine Quebec would want to be able to sign its own alliances.
They
technically banned military forces, but in reality between the toothlessness of the Continental Congress and the gaping exemption of, "but every State shall always keep up a well-regulated and disciplined militia, sufficiently armed and accoutered, and shall provide and constantly have ready for use, in public stores, a due number of filed pieces and tents, and a proper quantity of arms, ammunition, and camp equipage" (that's from Article VI) means that Quebec could really do pretty much anything it wanted as far as land forces are concerned. (That's beside the fact that the regular army was
tiny, so the institution wouldn't be all that important...or necessarily Anglo-dominated, if the Canadiens had made a significant contribution to the war) The Continental Navy OTL was retired for expense, apparently, so I don't know that Quebec, alone, could afford to maintain a navy.
And I don't really see what Quebec could possibly gain from being able to sign its own alliances. France is already an ally of the United States; Britain isn't going to ally itself with Quebec at this point, and in any case one would question the willingness of a no-Quebec Act Quebec to ally itself with Britain; and the thirteen or fourteen states closest to it are its allies by virtue of the Articles. So signing on has only upsides for Quebec (particularly since they would presumably be doing it during the ARW, not afterwards) in terms of alliances, while not signing on probably denies them alliances with the Anglo states (which have much greater manpower than Quebec, if funny ideas about how to run things) and gives them no real extra opportunities. Not to mention that it denies them a voice in how the war is being run.
EDIT: I'm not sure to what degree the well-known
modern attitude of Quebec towards Anglo Canada influences our perceptions of historical Quebec's attitudes, but it does seem that as long as some regard was given to Quebec's "peculiar institutions" that there might be some arrangements that could be come to, just as Quebec was more or less peacefully part of Canada for a century with, so I understand, little separatist sentiment.