Just a DP. I uploaded my ITIN via the Document Center page and the status was Pending. Out of curiosity, I went back in to the page about 3 hours later and the status had already changed to Completed.
To check if my ITIN had in fact been added, I went into the Authentication Management page but could not see any ITIN added there. It just has my email, mobile and passport number. I also tried calling and putting in the last 4 digits of my ITIN when it requested SSN but Amex could not locate my record.
I'm not sure if Completed status just simply means that they've taken the document and sent it off for processing, or if the request was actually fully completed (which would be record-breaking speed if so). If the latter, uploading your ITIN may not actually work.