It's certainly a plausible WI -- OTL, Arnold's campaign came pretty close to succeeding.
Two threshold questions arise:
1) Will the Quebecois join the Revolution?
Probably, but it's not clear how enthusiastic they'll be. The British treated them well enough. I suspect they'd declare independence, but not contribute much to the "common" cause. (Note that Arnold was authorized to offer the Quebecois equal status with the other 13 colonies.)
2) Would independent Quebec survive the Revolutionary War?
That's much less clear. Quebec was in a bad strategic position; the British controlled the mouth of the St. Lawrence River, and could move troops inland at will. Quebec City has a superb defensive position, but the rest of the province is quite vulnerable.
The question then becomes, would the British try to recover Quebec? After all, they do have other things going on. Still, one suspects they would. It's a vast province, and symbolically important as the biggest single spoil of the last successful war.
Note that, whether they do or don't, the RW jumps the tracks in a big way. There's no Saratoga. Some other battle may take its place, of course... but both sides will be moving troops in very different directions than iOTL. Still, IMO the most likely outcome is that the British recover Quebec but the Americans end up winning their war anyhow. Both US and Canadian history will proceed rather differently thereafter.
But say Quebec Libre makes it out of the war: either the Brits decide not to attack, or the expedition's commanding officer is one of /those/ generals, or they just roll snake-eyes. Whatever. Now what?
Well, I think it's likely that QL joins the Articles of Confederation. Why not? It's a loose federation, and they'll still have plenty of autonomy.
But by 1787 the wheels are visibly coming off the AoC. So there'll probably be a Constitutional Convention, much as iOTL. And now things get hinky and ginchy. Do the Quebecois even join? Or do they simply secede? I have trouble seeing much enthusiasm in Montreal for a More Perfect Union with the much more populous Anglo states.
Other hand, if Quebec stays in, this TL's Constitution may be very different from ours. (Just to give one minor example, Quebec most definitely has an Established Church.)
Again, I think the most likely outcome is that Quebec peacefully secedes from the Confederation when the rest of the country joins the United States. And I think it would be peaceful; the country was profoundly war-weary in the 1780s, and the concept of "Union" hardly existed yet.
Mind, this sets an example for future secession. It also means the map of North America looks rather different. The northeast corner of the continent is still British, and the Hudson's Bay Company will still be trying to claim the far northwest. What's now western Canada will eventually be the subject of a three-cornered dispute. My best guess is that Britain still manages to claim the modern Yukon Territory, while Quebec expands into most of what's now Ontario (though the US may grab the southern "tongue" east of Lake Huron) and Manitoba. The Pacific Coast, who knows.
If Quebec stays in, then at least there's none of this nonsense about having a Senate that's fair and balanced between free and slave. Quebec throws that out of whack from the start, and then it probably spawns a second and then a third Francophone state in the north. Quebecois would not be abolitionists, but they'd find the southern slave system deeply alien, and would have no interest in supporting it.
Assimilation, hmm. Probably not in Quebec itself. But there'd be some interesting mixing in the new western states. I suspect there'd be more movement south than north -- Quebec has more land, but it's /cold/ -- so by the mid-19th century there'd be Francophone minorities in Ohio, Michigan and Indiana.
Politically, the francophones would be natural Jeffersonian Democrats. I doubt John Adams even has one presidential term in this TL.
At this point the knockon effects really explode. The floor is open...
Doug M.