Mr. Edberg has answered me (my emphasis):
The font being considered for licensing as per the emoji4unicode posting [...] was not “Apple Color Emoji”, which was never considered for licensing. Rather, it was a separate black & white “Apple Emoji” font mainly developed as part of the proposal to Unicode and ISO 10646 for the addition of emoji characters, in order to provide glyphs for use in the code charts etc. As far as I know it is not a font that ever been included in shipping Apple products.
So the answer is that there is no license for 'Apple Color Emoji.ttf' available.
IANAL, by the way.
Update 2018-02-06: According to Twitter posts, Apple has started enforcing that now in the App Store. Sam Eckert reports there:
I’ve just been on the phone with the App Review team regarding the Emoji issue. Apps are NO LONGER ALLOWED TO USE EMOJI in non-keyboard based situations. Means if your app displays emoji anywhere without a user having it typed in, it’s illegal and will be rejected.
