As has been said, padjal will never be playable, as they're not even a true race - as Colorful mentioned padjal are actually born as hyur, specifically, Midlanders, but sometime in late childhood they are selected by the elementals to become their emissary in Gridania, which by currently unknown means (somewhat disturbingly referred to in version 1.0 as being 'touched' by the elementals) causes them to cease aging physically, trapping them in the body of a child while also simultaneously causing horns to grow from their heads. So basically, you can't be born as a padjal, it's more a special status where you're chosen to be one by the elementals.

They do seem to be able to take leave of the forest occasionally though (Kan-E is repeatedly seen travelling around Eorzea after all - including all the way to the Churning Mists in Dravania), so they're not necessarily bound to the forest eternally, they just have to exercise caution with everything they do is within the will of the elementals. Hence as adventurers are free-spirited and pretty much 'do as they like', it makes it pretty conclusive they will never be select-able as a player 'race'.