If there were to be a Greco-Israeli alliance, like the one that is speculated, then it would mostly serve in the same manner that the Greco-Turkish did during the Interwar Period, against Bulgaria, as a reaction to bilateral fears of Bulgarian aggression. In this manner, because Greece feared that Bulgaria would invade Western Thrace and Eastern Macedonia (and almost went to war in 1925 due to this paranoia, legitimate or not), and Turkey was weary of the possibility of Bulgaria invading Eastern Thrace and capturing Istanbul (a major reason why Ankara became the capital), they formed a block against that country. And it did work, it only took Nazi Germany with a million troops to break that alliance, and firm promises from their side towards Turkey that they were not invading Greece but merely expelling the Pro-British Greek Government.

There is no reason to believe that Greece is going to "go to war with Turkey" on behalf of Israel, especially given how since 1925-1926 no Greek Government has even contemplated to engage in revisionism over the Greco-Turkish border, treating the Lausanne Treaty of 1923 (and Greece’s interpretation of it) as gospel and manual handbook on how to deal with inter-state affairs. For a century the military dogma of Greece pertaining the Greco-Turkish border is strictly its perpetual maintenance and nothing more than that. To say the contrary, especially for attacking Turkey for the sake of Israel is on the level of conspiracy theories, while if Turkey invades first, they were already going to do so anyways (like the Axis doing so with Greece in WW2, for being too “Pro-British”, despite Metaxas’ promises for Greece’s neutrality being responded with demands to deliver territory to Italy and Bulgaria).