Personally, I think that while it's possible that Ebrietas is the current source of old blood for the Church, it couldn't be the original source.
She drops the Great Isz Chalice, which states that it's the first chalice brought to surface since the times of Byrgenwerth, and it's what granted the Choir audience with Ebrietas.
But in Byrgenwerth the holy medium that lead to the creation of the Healing Church was found, Willem advised his followers to feat the old blood before the Choir was granted audience with Ebrietas.
I think Oedon is more likely to be the original medium, since not only he's formless and represented by blood (so they literally found his old blood, instead of finding a giant alien and extracting blood from it), but also they created the Oedon chapel, where he was venerated.
She drops the Great Isz Chalice, which states that it's the first chalice brought to surface since the times of Byrgenwerth, and it's what granted the Choir audience with Ebrietas.
But in Byrgenwerth the holy medium that lead to the creation of the Healing Church was found, Willem advised his followers to feat the old blood before the Choir was granted audience with Ebrietas.
I think Oedon is more likely to be the original medium, since not only he's formless and represented by blood (so they literally found his old blood, instead of finding a giant alien and extracting blood from it), but also they created the Oedon chapel, where he was venerated.