The author’s question was about if Amazon KDP Author copies arrive in Amazon Packaging: Yes

The question behind it was about fulfilling orders from their author website via Amazon KDP Author Copies.

In general, this is not a good idea. Sure it saves the author from warehousing and packaging, but:
1. Author copies are supposed to be for authors. If they see you sending it to a lot of people they may flag the account.
2. The address you send it to is added to your account. That person probably makes other Amazon purchases to their address. So when they log on to Amazon to leave the book a review, they can’t because the system has now associated your two addresses.

USPS Media Mail via Stamps.com: https://www.anrdoezrs.net/click-100229582-10670063