The answer is yes.
Orthodox Christianity has a long history of Missionaries proselytizing and spreading the Christian Gospel to various cultures.
The first example dates to the 800's AD/CE, during the heyday of the Byzantine Empire. There were 2 Greco-Thessalonian Saints named, Cyril and Methodius. One of their major roles or "mission", was to convert the Slavs to Christianity; more specifically, the Slavic peoples living in the neighboring Balkan region, particularly around Bulgaria, whereby many Slavic peoples had settled beginning in the 500's AD/CE.
The Slavs, were originally a polytheistic pagan culture whose geographical origins were in Russia and Poland. However, by the 500's AD/CE-(about a generation after The Fall of the Roman Empire), many Slavic peoples conquered and settled throughout Eastern Europe, which at that time, was largely comprised of three major lands: Illyria, Dacia and Thrace-(though including Thrace as an Eastern European land, is debatable). The Slavs dramatically and irreversibly changed the demographic landscape of Eastern Europe-(as well as having invaded a sizable portion of the Greek mainland, including parts of the Peloponnese in Southern Greece).
After living in the Balkans for 300 years-(including a sizable portion of the Greek mainland), the Greco-Thessalonian Bishops, Cyril and Methodius had assimilated the Balkan Slavs into Byzantine rite Christianity-(what would later be called, "Orthodox Christianity"). As the Balkan Slavs adopted the Byzantine Christian religion and culture passed onto them by Saints Cyril and Methodius, it began to spread and influence the Slavs of Russia whereby the First Russian King-(or one of the earliest Russian Kings) adopted Byzantine rite Christianity at the beginning-(or near the beginning) of the 2nd Millennium AD/CE.
Though the Byzantines also brought their own form of Christianity to Africa, specifically, Ethiopia, centuries before the arrival of Cyril and Methodius. During the early years of the Byzantine Empire-(I believe in the 500's AD/CE if my chronological memory is correct), a Greek Bishop named Frumentis and his Missionary Entourage had introduced Eastern rite Christianity to the Ethiopians. Now, it should be noted that Ethiopia has a long historical connection with the Middle East dating to King Solomon; so the Early Medieval Ethiopian assimilation and conversion to Byzantine rite Christianity was not necessarily that culturally radical or shocking-(and relations between Greeks and Ethiopians predate the Byzantine era, dating back to the days of Homer).
And if my memory is correct, the Byzantines also conducted Christian missionary work in Nubia-(present-day Northern Sudan) centuries before the Sudan was conquered by the Arab Muslims. In other words, "once upon a time", Northern Sudan, was Christian, specifically, Byzantine Christian.
There were perhaps other regions within the Byzantine Empire whereby Missionary activity may have occurred; places, such as Sicily, parts of North Africa, as well as the Middle East. However, Byzantine Christian missionary work within the Balkans and East Africa during the Early Middle Ages is well documented.