Rome has reunified with some of the Eastern Christians; I think that's about as far as it will go. The remaining Orthodox will never submit to the Eastern (Catholic) Patriarchs, and Rome certainly couldn't expect the Eastern Patriarchs to submit to the Orthodox hierarchy.
I don't think unification is all that critical. If 8 in 10 Russian pregnancies results in an abortion, you have to wonder about the future of Christianity in some of those countries anyway.
Care to cite a modern & reputable source on that?