Quebec rebellion with American support?

Just wondering if it would have been possible for French Canadians to rebel against Britain sometime after the war of 1812 and get US support but without the US planning to annex Quebec. Sort of like how the US helped Cuba get its independence.
 
I doubt that the US would go out of its way to antagonize the British. The British are at the peak of their power for most of the 19th century, and the US has nothing to gain by supporting an independent Quebec.
 
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