Yes, I believe your are correct.
As taken from http://www.olivierdeprovence.com/olivier%20anglais/symbole.html
Symbol of longevity and hope, the olive tree is renowned eternal. So was described Hérodote "The olive tree was burned in the fire of the temple by the barbarians; but the day after the fire, when the Athenians, charged by king to offer a sacrifice, rose to the sanctuary, they saw that a high shoot of a cubit had sprung from the trunk". In all the Mediterranean pond, one meets olive trees millenniums, and sometimes even considered pluri-millenniums. He is the witness of our history and accompanies him all the time.
_______Symbol of peace and reconciliation, the branch of the olive tree is chosen by God to mean to Noé that the Flood is finished and that the diminution begins, symbol of the forgiveness.
_______Symbol of victory, the olive tree is a present loaded with a gratifying meaning during the Olympic Games in Athens. Crown of olive tree and jars of olive oil are so offered to the winners.
_______Symbol of force, the olive tree is renowned for its very compact, very heavy and very hard wood. It is wooden of olive tree that are made Hercule's bludgeons and it is with the wooden picket of olive tree that Ulysses brings down Cyclops in the Odyssey.
_______Symbol of allegiance: it is wooden of olive tree that the Ulysses's and Pénélope bed is made, reads who will welcome none of the numerous pretenders in the realm of Ithaca, during the twenty years of absence of the Greek hero.
HOWEVER... and more importantly
as taken from http://www.christenundjuden.org/en/displayItem.php?id=104
The Olive Tree – Symbol of Jewish-Christian Relations
For Reflection
The olive tree is a biblical symbol of Israel. Two big branches grow out of the same trunk, symbolizing Judaism and Christianity both developing out of biblical Israel. Other branches growing out of the two main ones symbolize the diversity of Judaisms and Christianities.
AND as taken from http://www.bus.ualberta.ca/yreshef/zionism/symbols.html
The Olive Branches:
The emblem of Israel shows the Menorah surrounded by two olive branches. The prophet Zechariah, who lived in the sixth century had a vision. He saw a golden seven branched menorah flanked by two olive trees. Our Rabbis interpreted this vision to mean that the Temple and the State of Israel would someday be restored to their former glory. Also, olive branches are symbols of peace.
: Pope Benedict waved an olive branch at the crowds when he was first
: presented. Maybe all new popes do this. The "olive" is also
: supposed to represent that the penultimate pope is a lackey of
: Israel, I've heard.
: The second-to-last pope is only supposed to be around for a few months,
: probably murdered.
