If you mean memberships or so, some of mine have not been shown for years yet they work fine.
Amex offers should be available in a week/month if you are actively using the card.
I think now it's a card they offering you free and want you to carry balance/installment plans for revenues since they can't do it with the charge... Not sure how's the work in reality though.
My first ever rejection is the plat as well. Although they give me the card after resolving an issue with mistakenly recorded default in their file for me (and which is not in credit files from Equifax and Experian).
I think it should be fine, yet they may approve you a lower than expected credit limit...
I am no expert but i do see an "age of credit file" saying 6 years + on my credit report...