Well, it's a mystery gift pokemon... I'm guessing that's the same thing? It involves picking it up from a pokemon center from an NPC, so synchronize won't work with that? I was told it would work...
The chances of you getting perfect IVs by the deadline depends on how quickly you work and which stats you want perfect IVs you want. Legendaries in Gen 6 are more likely than not to have 3 perfect IVs if I remember correctly.