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I believe it does . In the US posts fro. 2018 indicate as much but you have to add it in your accepted payment types in QB.
As of middle of 2019, again from community posts, AMEX in Canada can be used to pay your QB subscription but not to receive customer payments.
Of course all the above could be out of date
Using the GoPayment app and bluetooth card reader, I had no problem processing my customer's American Express card.