Is it possible to add AppleCare without activating a device?

Hello Emmielouux3

You question hasn't been answered in over a day so I thought I might have a go.

From what I have found you must have the phone on and active to be able to register it for AppleCare+

There are a couple of ways to enrol the device in an AppleCare+ plan, but all of them require the device to interact with Apple as part of the process. This webpage describes is well. It shows how to buy AppleCare+ from the iPhone, via an Apple webpage, on the phone, or in-store. To summarise:

• If on the device, clearly it must be active.
• If on the web, the device must pass a diagnostic test.
• If in an Apple Store the staff will inspect the phone.
• If via a call to Apple and the device must pass a diagnostic test.

This leaves you will little option but to activate it.

You also have another thing to ponder and that is the Apple Account to which the device will be attached. You don't mention the age of your son, what other devices he has, or if he has an exiting Apple Account. The best practice is for each person to have their own Apple Account. If your son is old enough to be in control of his own account even if you have his credentials you might find it a challenge to register the device to his account without his knowledge.

There remains the possibility of registering the AppleCare+ plan on your Apple Account (which as I mentioned above is not ideal) and at some later stage transfer the AppleCare+ plan to the device when it is signed into his account. Apple seems to allow this. See Transfer your AppleCare plan - Apple Support

However, all of the above requires you to open the box, activate the iPhone, and set up AppleCare+

See also Apple's page AppleCare Products - Apple

I always purchase AppleCare+ on my iPhones that I obtain directly from Apple's online site. If I am trading in an iPhone with any AppleCare+ balance, I call up AppleCare and get a punctual pro-rated refund before they cancel the AppleCare+ coverage that is tied to that specific phone serial number. By punctual, that means that within 7 days I will see a refund on my credit card, or if requested, they will send a physical check.

Long before my new iPhone 16 Pro Max was physically delivered last fall, it had AppleCare+ coverage tied to its serial number which AppleCare got from the order information, not from me. In your case, you may only need to provide the serial number from the 16e box when requesting AppleCare+ (which is now a subscription) coverage.

Best to contact AppleCare and ask them specifically what they need from you for post-purchase coverage. At the bottom of this AppleCare/iPhone page, is three options for how to buy.