Originally Posted by bgriff

If you were able to add both to a single card, likely yes, based on the way Amex typically allows double-dipping across other promotions and credits. I'd be surprised if you were able to do that though. In my experience with pairs of offers like this I often have the points option on my Platinum card and the cash option on other cards, but I don't think I've ever had both offers of a pair like this on the same card. Check the terms to make sure that they're not applicable under different circumstances or to different types of product (like sometimes Marriott and MGM Resorts will have pairs of offers where each offer is only valid for certain brands/properties).