If the experience of the Melkites is any indication, then no, the Ukrainian Church will not be the first to unify. When the Melkites attempted “dual communion” with both Rome and the Antiochian Orthodox Church (and through them all of Orthodoxy), Rome stated that there cannot be communion between two particular Churches without communion first being established between all the Churches. So if Rome is to be taken at its word, then communion must be established between Catholicism and Orthodoxy in general before there can be a united Ukrainian Church, unless of course either the Ukrainian Catholics leave the Catholic Communion for the Orthodox Communion, or the Ukrainian Orthodox leave the Orthodox Communion for the Catholic Communion.

I don’t necessarily agree with Rome on this one, but that’s the way it is.