The Greek Royal Family, which DOES EXIST (sorry HRH Duchess of Windsor), does not reign or rule anymore. The Greek people voted to get rid of them back in 1973.Although, King Constantine II never abdicated he is considered a pretender.
Now to answer the question......
No. The current Greek Royal Family does not go back to 1200 BC. It only goes back to 1863. In 1863, The House of Schleswig-Holstein-Sonderburg-Glücksburg began in Greece with George I as the new "King of the Hellenes". George was born a Danish Prince.
The Danish Royal Family is an extension of the UK Royal Family. The King of Greece, Constantine II, is the line of succession to both the Danish and British thrones. He is a 1st cousin, once removed of another member of the extended Greek Royal Family----Prince Phillip, Duke of Edinburgh and wife of UK Queen and the brother of another---Queen Sofia of Spain, wife of Spanish King Juan Carlos I.
Also Constantine, Sofia, and Phillip are descendants of Queen Victoria of the UK and Constantine and Sofia are descendants of Kaiser Frederick III of Germany making them members of the defunct German Royal Family. This means that all 3 are in the line of succession to the UK throne but they're like in the 500s. Phillip was #521 a month or so ago but the number changes almost constantly due to births, deaths, or marriages to Catholics of the people in the line which officially extends to over 1000 people. Although Constantine and Sofia are in the line of succession to the Danish throne, Phillip renounced his place in the line of succession to both the Greek and Danish thrones and renounced his Greek citizenship in order to to become a British citizen. He did this to make himself more palatable to Elizabeth's parents and get their approval to him marrying Elizabeth.