As of today, I still haven't gotten any confirmation emails for my Emblem or a shipment email for my Braytech Werewolf shirt, of which I purchased a week ago, I checked all the correct emails that I've linked to purchase the shirt as well as the email I've connected to my Xbox account as well as my Bungie account and all checks out, but haven't received any Follow up emails except for the confirmation of my purchase for said shirt.
-
Don't know about the emblem but the shirt said it wouldn't ship out until 4 or 5 weeks after you purchased. Hope this helps you out a bit!