Very poetic, but no such doctrine in the Church as "in the Church by desire for unity". Whatever you got that idea from, has no basis in dogma, doctrine, or tradition, it is a novelty.
All an Orthodox has to do to have efficacious sacraments is to become a Catholic, or as many Orthodox likely do in places where no Catholic mass is available, they accept the authority of the pope and have a willingness to submit to anything required to be called a Catholic. It's that simple. There is no need to invent another path.
Desire for unity is sufficient to bring individual people in the Church as we see in the doctrine of baptism by desire, for example. But in this case, since the only heresy in Orthodoxy is persistence in schism, desire for unity removes the heresy. It is not a dogmatic novelty.
It is true that individuals may convert now, and some do (I did). Still, it would please God Who prayed for unity so fervently (John 14), for the Churches to unite corporally.