Mine is trying to find a frickin Japanese Magikarp on the GTS. Why? Because you get people who want lvl 100s for a lvl 1! And then there are the Legendaries that are always requested! It never fails!
And another thing: I got a Shiny Event Eevee from the VGC, but it didn't add Eevee to my Pokedex!
If you want an Eevee for the pokedex you could simply get the Eevee from Bill in Goldenrod. =p