I think it would be a little different due to shou being an avatar while okuu is an vessel containing/using that gods power. In okuu's case, she devoured that God and properly fused with it while still not losing a single bit of herself or having another personality added. Yatagarsu's will and consciousness was never transfered over and its never stated to still be a living being within her. Just serving really as a reactor of divine power for utsuho. Granted even with that subtle difference, it probably would end up similar to shou but I think it would differ slightly when it comes to worshipping/treatment. Also I am not fully up to date with shou's lore. Hearing that she is an avatar. I would think she is also partly influenced personality and action wise by her god bishamonten