No, the Greek Orthodox church is a part of the Eastern Orthodox Churches.
Greek Orthodox Church of the Annunciation was created in 1769.
Catholic AnswerThis is known in the Catholic Church as apostasy and is an automatic excommunication. If there is something you feel drawn to in the Greek Orthodox Church, then you should look into the Greek Uniate Church with is the part of the Greek Church which has always been in union with Rome (even after the Greek Orthodox left the Church). You may attend Greek Uniate Sacraments with no special permission, but to officially change Rites, you would need to apply to your Bishop and their Bishop.
Eastern Orthodox Church (or the Christian Orthodox Church).
The Romanian Orthodox Church mainly follows the liturgical practice of the Greek Orthodox Church, rather than the Russian Orthodox Church, such as the use of the new calendar.
You get baptised and get married in the Greek Orthodox Church
The present archbishop of the Greek Orthodox Church in America is Archbishop Demetrios.
Greek Orthodox Church of the Holy Trinity was created in 1953.
Profitis Ilias Greek Orthodox Church was created in 2008.
The Greek Orthodox Church was brought to Australia from the demand of Greek immigrants migrating to Australia in the middle of the 19th century and the foundations of the Greek Orthodox Church were then laid on 29th of May, 1898.
Macedonian orthodox like Athenian orthodox and Thessalian, Epirotian, Thracian orthodox can all marry in the Greek Orthodox Church no matter where in Greece they hail from. The foreign church of the Former Yugoslav Republic is a schismatic church and not recognized by the ecumenical patriarchy of Constantinople as an orthodox church. Therefore no Greek, whether Macedonian, Athenian, Thessalian etc can marry in the church of the former Yugoslav Republic but the various ethnicities of the Former Yugoslav Republic who follow their Christian church can marry in a Greek Orthodox Church.
There are several articles linked from the Greek Orthodox Archdiocese of America's "History" page which address the history of the Orthodox Church in general, and/or the Greek Orthodox Church in particular. See the link below.