Honestly, I don't exactly know myself. The only example from OTL is Ecumenical Patriarch Meletius IV who was a Metropolitan Bishop in the Church of Greece before being elected Patriarch of Constantinople in 1921. After the Greek defeat in the Greco-Turkish War of 1919-1922 he was forced to resign and ever since π) has been separated from the Church of Greece. I would assume that if Greece ever gets a hold of Constantinople for any period of time ITTL they would merge the Church of Greece with the Patriarchate, but I'm not completely sure.
We should not confuse 1830 with 1920 here. The patriarchate had long reconciled itself with Athens by then and had pretty close ties with it, hardly odd when it was for every practical purpose Greek in nature. In such terms it was hardly odd that the church of Greece not at all accidentally did NOT have an archbishop, till after the Asia Minor disaster and the bishop of Athens was just presiding over the holy synod. I think it's a fair guess that if Greece had come to directly control Constantinople the church would had gotten reabsorbed. ATL you also have the minor complication of Crete being her own separate archdiocese.