Absolutely. The Orthodox Church consistently refers to herself as the Catholic Church through all the centuries. Here are just a few examples from the Encyclical you mention…
Encyclical of the Eastern Patriarchs, 1848
A Reply to the Epistle of Pope Pius IX, “to the Easterns”
To All the Bishops Everywhere, Beloved in the Holy Ghost, Our Venerable, Most Dear Brethren; and to their Most Pious Clergy; and to All the Genuine Orthodox Sons of the
One, Holy, Catholic and Apostolic Church
… the many great and glorious Fathers of **the Catholic Church **in all parts of the earth, [they mean the Orthodox Church]
… which
the Catholic Church, even from her infancy, taking unto her the whole armor of God, and assuming the sword of the Spirit, which is the Word of God (Eph. vi. 13-17,) has been compelled to combat
… for the orthodoxy of
the Catholic and Apostolic Church
… contrary to the universal Confession of **the Catholic Church **
… Wherefore the
One, Holy, Catholic, and Apostolic Church, following in the steps of the holy Fathers, both Eastern and Western, proclaimed of old to our progenitors and again teaches today synodically, that the said novel doctrine of the Holy Ghost proceeding from the Father and the Son is essentially heresy, and its maintainers, whoever they be, are heretics, according to the sentence of Pope St. Damasus, and that the congregations of such are also heretical, and that all spiritual communion in worship of the orthodox sons of **the Catholic Church **with such is unlawful.
The whole Encyclical is here…
fordham.edu/halsall/mod/1848orthodoxencyclical.html