I'd never thought of this, but upon reading your post, took a quick look at my Amex account. I can only see it for cards I have. Also, recently I looked at the QF Ultimate card. And whilst it had some good opening offers, clearly stated that most (if not all) were not available to current Amex card holders. So, that would indicate to me, that the answer to your question is most likely going to be a no.
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