No, because the British colonies in Canada were much younger than the 13 American colonies. Britain only threw the French and Spanish out of North America at the end of the Seven Year's War (what the Americans called The French and Indian War) and that was so recent that George Washington (among others) had fought in it.
The American colonies had been self-governing, self-taxing, semi-autonomous societies for over 150 years by the time the Stamp Act was introduced in 1765 - the first attempt by Parliament in London to directly tax the citizens of the 13 Atlantic colonies. That's what began the long, slow, process of moving the colonies toward independence - what the Americans saw as an attack on their rights as
Englishmen. As far as they were concerned, their colonial governors and local assemblies reported to the king, not to a Parliament in which the Americans had no representation. It was only after King George himself declared the colonists to be rebels and their leaders traitors that independence came to be seen as a serious option.
There was simply no corresponding political situation with the relatively small Canadian colonies that would have produced a similar result.
Also don't forget that even in America no more than about 1/3 of the population was ever actively pro-independence. (There was more support for the anti-British action of 1775 and 76
before independence was declared.) Another third was neutral and the remaining third remained loyal to the British crown. Many of them emigrated to Canada after the war, others went to England.
When I saw the title of this thread I thought you were going to ask about Benedict Arnold's "missed it by that much" attempt to conquer Canada and turn it into the 14th colony early in the war.

Regards,
Joe