Selling MacBook with Annually Renewing AppleCare

There are several threads like this one that discuss selling your used mac with remaining fixed-term (3-year) AppleCare. My question is about selling a used MacBook with annually renewing AppleCare+.

According to AppleCare+ agreement, you can not transfer an annually renewing AppleCare+ agreement to a new owner. However, Apple Support tells me that the agreement is tied to a MacBook serial number. Even though I can't technically transfer an annually renewing AppleCare+ plan to an eBay buyer, the buyer would be able to leverage AppleCare+ and all its privileges for the balance of my current annual term.

The annually renewing coverage on my MacBook is due for auto renewal in a month. If I sell my MacBook today, remove the MacBook from my Apple account, and if the buyer adds the MacBook to his or her Apple account, would the auto-renewal of my AppleCare+ plan still go through in a month? I know I have the option to cancel the auto-renewal. But I'd like the buyer to have peace of mind with an extra year of AppleCare specially when the buyer is willing to cover my cost for AppleCare renewal. Apple support has not provided a clear answer on this. Appreciate any insights.