My impression was that adding a CDP made the system use that rather than the Amex Plat one (which is already pre-loaded into your account as the default one to use if you received #1 Gold via Plat). Certainly when I tried a different CDP to see how it compared it seemed to remove the 4h benefit and tip me into a 2-day rental. Easiest thing to do is probably just open a couple of separate browser windows and run through different variations - not logged in, not logged in with AAA CDP, logged in with AAA CDP, logged in no AAA CDP, etc. and she what comes back! Overall I still find the Plat one pretty good, but then I'm UK-based so don't have access to AAA discounts.