This thread is incorrectly titled. It should read "An Orthodox Christian people north of the Caucasus" or "An Eastern Orthodox Christian people north of the Caucusus" unless of course this thread was referring to settlement by ethnic Hellenes of Orthodox Christian faith in the region. Eastern Orthodox denotes a religious group as does Roman Catholic. Greek Orthodox should be understood in the sense of Irish-Catholic.
(Of course, I am aware that unlike the RCC, the Eastern Orthodox churches are not as unified, being somewhat autnonomous and quite decentralized. That the Ecumenical Patriarch is not a Pope, and there are many national (or ethnic churches), so in reality the situation is not as simple, but in principle, while any one can become an Othodox Christian, one must be Greek (or Serbian, Russian, etc.) to be Greek Orthodox (or Serbian Orthodox, Russian Orthodox, etc.) just as Irish Catholics are by definition of Irish descent.)
For a people to be Greek Orthodox, they would have to either be Hellenic or else integrated into a Hellenistic empire. Non-Greeks living under Byzantium, the last Greco-Roman empire, might be considered Greek Orthodox in the sense that they belong to the national church, under the Patriarchate of Constantinople (also, despite not being ethnically Greek, they would be fairly Hellenized in language or culture but of disparate racial or ethnic origins). Remember what I said about Eastern Orthodox Christendom not being centralized like Roman Catholicism, and the various national churches. Because you appear to be mentioning Kipchaks (a non-Greek people) from north of the Caucusus (an area outside the Byzantine world), they would not qualify as *Greek* Orthodox in either an ethnic sense or as part of a Hellenistic empire.
(By Greek Orthodox you might instead be referring to liturgical language as opposed to ethnic affiliation, but note that unlike the Roman Catholic church which prescribed Latin as the official liturgical and scriptural language until recently, Eastern Christendom made no such language requirement. There is no reason why medieval Greek, the dialect in use by the Byzantines, would have to be the liturgical language over Old Church Slavonic or any other language.)
So what is the point of all this nitpicking? Well if you really mean an Orthodox Christian people north of the Caucasus, then this might not be AH at all, as many Georgians and Russians were Orthodox Christians. I do not know what religion the Kipchaks followed...