Why would it have made any sense for the British to try to invade the Union if the Confederacy had won its independence? The Union had a gigantic army — far larger than anything the British could have amassed in Canada. Given half an excuse, the Union likely would have “liberated” the Canadians from monarchical government, as was tried during the Revolution (for real) and War of 1812 (as a bargaining chip — purportedly).
If the Confederacy had won its independence, how would the British have invaded the South from Canada?
I’ve never heard of any of this. I think there’s a reason for that.