I used CAP and submitted multiple applications for the Gold Card in July. I wasn't prequalified for it, or for anything else, at the time. Granted, that was a weird situation that probably doesn't include any useful information for other applicants. I haven't even ever explained just how weird it got (I had a conversation with the CEO of Amex ...)
But, I was referring to the prequalification I started seeing in August for the Delta Gold card. I applied based on prequalification and was denied. I should note, I did not see "KJ, you are preapproved!" when I clicked to apply. I called and requested reconsideration. A week later, I got a letter in the mail saying they stood by the denial. The day I received the letter, I happened to click Apply on the Marriott Bonvoy card. I wasn't really planning to apply, I was just looking around. I noticed for the first time "KJ, you are preapproved!" at the top of the page. I stared at it for a minute, then went to the Delta Gold card and clicked Apply. Same thing, "KJ, you are preapproved!" Every cobrand credit card said the same thing. Core cards still said "KJ, applying to expand your membership with us is easy" or whatever. I went incognito and checked prequalifications, and Delta Gold showed up. I applied and was approved. The next day, I checked prequalifications, and there was nothing listed. I checked preapprovals, and all the cobrand cards still showed preapproval. I applied for a Hilton card and was approved.
So, I don't think that was due to the CAP and other craziness that taints my DPs on the Gold Card. I honestly do not think that prequalification relates to credit scoring, at least not very much. That said, most people who prequalify probably also would be preapproved, because most people with solid income who would be interested in applying for an Amex probably have decent credit. For anyone with doubts, though, I would caution against taking prequalification seriously. I think preapproval is where it's at with Amex. Prequalification is just for possibly better SUBs, in my opinion.
The caveat is, though, that I can only speak to my personal experience, which may be unusual in some ways ... YMMV.
as soon as i got a fico score i was pre-approved for every card amex has, they don't seem to care how long your history is. you might even be able to get approved with less than 6mo of history, but you'd probably have to cold-app without a prequal that early. if your score is good and you don't have tons of inqs and new accounts you should be approved.
when i got my card, the pre-approval signup bonus was less than the max offer, so i apped using incognito and got $50 more.