I think Jaws of Hakkon revealed so much about spirits and fade and power that explained how can having so many believers in anything in Thedas, would reflect in forming strong equivalent in the fade, and bring such power in the world of dreams.
So yes, the faith plays important part in this world the dragon age writers created, and the divine have significant meaning in Thedas and the Fade, like how Hakkon formed first time, and Avvar keep forming him many other times again. Not the same entity, but the same concept.
It's not newly introduced concept to DA actually , DA:O had the spirit of the forest, who was "formed" somehow ..
A reflection for things/beings/meanings/feelings of the mortal world in the fade, that's most of the strong spirit are. So the Divine you meet in the Fade, it's that. Maybe not only Justinia, but all the divines accumulated over the ages. Or even if she is Justinia, the spirit didn't form upon her death, but upon her coronation most likely, and she watched, and fed from all the faithful and from the Divine herself, making her that strong, and that helpful, and that faithful.. Not strong enough to beat Cory on her own, but enough to be the catalyst of his demise, helping the inq, twice. Or maybe even more, by letting people think he/she is herald of Andraste .. etc?