It would appear that the HA Pokémon without overworld sprites have the standard xor PID check in place. (Eevee, Deerling as well as Zorua).
The other standard gift Pokemon without overworld sprites such Happiny (egg) and Magikarp do not have this in place.
Source
Project Pokemon is a large ROM hacking platform with some of the most knowledgeable people in the game.
This means that the Eevee is shiny locked, along with the other HA gift Pokemon.
This is literally the only slightly credible source on the internet I challenge anyone to find better information.