Yes and no. The Eastern Churches have their own theology and it has a different notion about the fall. In the West, this event in Salvation History is explained by the concept of Original Sin. In the East, it is explained by the concept of Ancestral Sin. The former implies an inherited guilt, while the latter implies an inherited wound. Therefore, the doctrines are not the same. Unity does not mean uniformity of doctrines.
Both the East and the West agree that the Virgin Mary has never sinned, that she’s always been unstained by sin or immaculate. Now, in the West the doctrine of Original Sin creates a problem that is resolved by stating that Mary was spared inheriting our foreparents’ sin at her conception. In the East, this problem doesn’t exist with the doctrine of Ancestral Sin.
Personally, I prefer the Eastern doctrine. Not only is it simpler, requiring no other doctrine, but it also elevates Mary’s virtue even higher. Of my own, keeping in mind that “what has not been assumed has not been redeemed” (St. Athanasius), I also think that conveys the idea of a more complete redemption of man by Our Savior, since he assumed not a special human nature granted by privilege to the Mother of God, but the very same as mine which I find nailed to the cross and then risen from the tomb.
However, neither doctrine was revealed, but are theological conclusions based on Divine Revelation, yet inferring the gaps. In this sense, humility demands that the Churches of the East and of the West acknowledge the right of the other to hold their own doctrines and to not contradict them.