If
General Richard Montgomery doesn't die and wins the Battle of Quebec in 1775, then a few major changes happen:
Francophone, Catholic Quebec likely becomes part of the early independent colonies. Would they be an independent state? Would they become part of the new Union? Would they be allowed by the other States to refuse to sign the Articles of Confederation? Would there even *be* an Articles of Confederation - if Quebec eventually participates in the Second Continental Congress, how would that impact the drafting process?
This, naturally, butterflies Canada. IRL all the Anglo loyalists in the newly independent states move to Canada and create that new identity, but that doesn't happen here. Do the Anglo loyalists leave back for Britain? Go to Australia? If they stay, and I assume many would, how would this affect the post-Revolutionary political system in America?
Finally, assuming Gen. Montgomery survives the rest of the war, George Washington might not become the famous general and war hero that he was. How would this impact American political history? Would Montgomery get elected as the first President?
Well you haven't addressed why the Canadiens would become interested in staying with America, and this particular scenario peculiarly sets up further problems.
Montgomery pulled off a really good victory as is, and it would be neat if he had captured Carleton, but he left David Wooster in charge of Montreal and Wooster was a terrible administrator. Schuyler failed (and it was a far hope) to convince all the Iroquois to sit out the war, so when Wooster saw a minority of Iroquois helping the British, he treated all the Iroquois as enemies. The Iroquois were prominent trading partners with the Canadiens of Montreal, and so when you combine his overbearing administration of Montreal, and the harassment of their trade with the Iroquois then it is no surprise that the Americans gained very little traction among the Canadiens in Montreal. Despite this bullshit, the Canadiens contributed militiamen to the Patriot cause - which makes alt history very alluring at this point.
As an aside, even after the Americans were booted back into the wilderness of Upstate New York, most of the Iroquois sat out the Revolutionary War. Joseph Brandt, the partial ancestry Iroquois warleader, couldn't talk the Iroquois into joining the war. Which creates another interesting alt history perspective, but but but but (and I actually stuttered as I was thinking this part aloud) it's a Human issue of very great concern. Arguably the American concept of confederated states was greatly influenced by the example of the Iroquois. The Patriots launched the genocidal Sullivan Expedition as repayment for Joseph Brandt's warband. And it was genocide, with an explicit purpose of destroying the homes and food supply of the Iroquois as a whole at the onset of winter with the hope that it would make them suffer so severely they would be unable to engage in future warfare. Some of the Founding Fathers questioned how they were going to be viewed by the descendants for that Expedition, doubting its necessity, and worrying that whatever good would come out of the Revolution would be completely overshadowed by this sin.
The siege of Quebec City was really unpleasant, and when it was lifted the British treated the place pretty well. Carleton was a really good Administrator, and in my opinion he kept the Canadiens out of the war. When the British crushed the American liberation of Montreal, and reoccupied Montreal, conditions improved for the people there and they were treated better. I hope no one's eyes crossed while reading that sentence, but that is how screwed up the Canadian Campaign was.
If Montgomery takes Quebec City, Wooster will still make a mess of things in Montreal, and it is very likely a comparable administrator would make a mess of Quebec City. And even if the Patriots possessed Quebec City and Halifax, well the amount of soldiers the British sent over was definitely capable of taking these places. And if the Americans did much better after Satargoa, and launched a second campaign into Quebec, they would have a long and barely supported slog up through Canada. So the Americans would likely have to win these places in the peace talks.
I think there is a path for Quebec to become an independent state, and I think there is a path for Quebec to join the Articles of Confederation as a fully equal member. There is even a path for a super positive early American victory in the Revolution. Yes, there would be an Articles of Confederation, even if the Canadiens sent delegates there before it was ratified and they objected, there would still be an Articles of Confederation. The Canadiens would probably want Article 3 to include wording that would provide for a stronger protection of state religions, and a recognition of their language. The official language of the Continental Congress would probably be English, but there is no way free Canadiens would consent to having their culture changed when even the occupying British didn't do that. A clause requiring unanimous consent in the organization of commonly held territory would likely be important to the Canadiens as well. Going forward into the Constitutional era, the Canadiens would force the Constitution (or the heavily amended Articles of Confederation) to be much more biased towards state rights. There might even be an explicit clause about secession - no matter what you think about that issue, we can agree that a secession process is not explicitly stated in the Constitution.
To determine the destination of the United Empire Loyalists you must address what happens to Nova Scotia and Newfoundland. If they stay in America there is going to be a lot of rancor, and probably a civil war. I think there was a way to reincorporate them into American society by having them go to Canada as in OTL, but then incorporating Canada at a later point - but this is a different discussion.
Correct me if I am wrong but weren’t there also a sizeable minority of English settlers or was that after arw when the loyalist fled
There were Yankee settlers in what would become New Brunswick.
If Montgomery survives, he will be famous, but he will not overshadow Washington.