If I want to issue an AU on my Amex TU, does the AU need to be a member of Costco?
Yes, additional cardmembers must be Costco members. In fact, you'll be asked for the additional users membership # and the card will not be approved or sent until Costco verifies that the applicant is an active member.
I have been trying to add my gf to my Costco TE card for nearly 2 months for this very reason. When I got the card, I was a secondary member on my father's executive business account. After getting my own membership and adding my gf to the account, I requested an additional card for her, and the request was denied because her account was not linked to my father's account. I needed to change the Costco account associated with my TE card before I could add her as an additional user.
Whatever you do, if you request an AU card for the Costco card, do so in the store. Otherwise, you'll have to wait a couple of weeks if you apply online, just as with the primary card.
No hard inq that I'm aware of, but I believe that they do soft the AU applicant, because AmEx holds AU's responsible for purchases made on their card.