I’m not sure. I’m having trouble finding exact figures.
This is a bit of an overstatement. Mass., Va. and R.I., among others, had religious-freedom provisions in their laws, IIRC. Catholics served in the Continental Army with distinction and their service was appreciated. George Washington forbade anti-Catholic pranks or demonstrations by his troops.
Weren’t the Articles of Confederation superseded by the Constitution? Or is Canada actually still pre-approved (sounds like a credit card offer) under current U.S. Law?
(I’m sure you were joking above, but this is GQ, where we thrive upon nitpicking.) 
It might be a bit of an overstatement, but it is not much of one. Religious freedom laws tended to permit worship while not guaranteeing full rights as citizens. Washington would not have had to forbid anti-Catholic demonstrations, (an act that was partly prompted by the need to refrain from offending von Steuben, Lafayette, Pulaski, Kosciusko, and other Catholic European volunteers), if there was not already a general anti-Catholic bigotry among the troops.
There was no ongoing and persistent persecution of Catholics, but there was enough open hostility, (well demonstrated during the recent unpleasantness ending in 1763), that the Quebecois were pretty well aware of it.
If you’re talking about the Canadian Confederation talks in the 1860s, as MikeS points out, the Articles of Confederation were superseded by the current United States Constitution in 1789, so the offer was moot by then. Add to this the fact that the Canadian Confederation talks were held against the backdrop of the American Civil War, and during that time there were also raids on Canada by Fenians (Irish nationalists) coming from over the US border, so Canadians felt the need to protect themselves from the US rather than join it.
This said, remember that during the Rebellions of 1837-1838, many of the rebel leaders were in favour of having the Provinces of Upper Canada and Lower Canada join the US. So there was a strong pro-American sentiment among liberal Canadians at the time. Even if the rebel forces had been strong enough to defeat the British Army – they weren’t even close, though the Patriotes did win one battle – I’m not sure if the US would have considered the offer. Admitting two new free states at that time might have been politically unfeasible.
But to answer the question in the OP’s title, if there is one major effect the American Revolution had on British North America, it was to convince the British to grant the colonies legislatures. New Brunswick was split from Nova Scotia in the 1780s and both colonies were granted a legislature, as were Lower Canada and Upper Canada when they were created from the Province of Quebec in 1791.
I’ve heard that a major reason why the American colonists were angry about the Quebec Act 1774 was that it expanded the boundaries of the Province of Quebec beyond territories in the American Midwest that the Americans were planning to colonize (see Captain Amazing’s map), while at the same time granting civil rights to Catholics in the Province of Quebec. There was some anti-Catholic rethoric used to fire them about this issue.
That was a major reason. Also, part of the reason the civil rights to Catholics sections in the bill aroused such opposition in the American colonies was an accident of timing. At around the same time Parliament passed the Quebec Act, it passed a series of acts called collectively the “Coercive Acts” to punish Massachussetts Bay for the Boston Tea Party. The acts closed the Port of Boston, took away a lot of the rights of the Massachussetts assembly, allowed the Governor to move trials of government officials accused of crimes if he thought they couldn’t get a fair trial in Massachussetts, and allowed the army to quarter troops in barns and stables and other such privately owned outbuildings.
So this juxtoposition was used as a rallying cry…sort of a “Look at how Parliament rewards Catholics and Frenchmen, while taking away the rights of good Protestant Englishmen.”