I think the Turks will fight Greece again during the Arab Israeli wars with terrible consequences. It's more that the Turks won't be able to let WWII slide until they're truely crushed.
Turkey won't be able to intervene by 1956 that the Suez Crisis will occur, as most of their nation infrastructure & industry etc would be in ruins, their poverty stricken WWI & WWII veterans scars acting as a constant reminder of the terrible consequences of full scale war, throughout the Turkish society, while the political leadership, more than likely installed or at the very least approved by the allies, similar to post war Germany, where it underwent the denazification process, so Turkey's politicians will be decisively more liberal & pacifistic, at least in this date. Bottomline, Turkey will be outraged about it, but there will be nothing that they could possibly do about it.
However, the 6 days war in 1967 & the Yom Kippur War in 1973, I can definitely see some Turkish involvement, limited or not. They would have well recovered by that point, however, do not expect ATL Turkey to be anywhere near their OTL demographic figures, for a Turkey that has lost Eastern Thrace, (Imvros & Tenedos), Smyrna Zone, Biga, Caria & Bithynia on the west, as well as Greater Armenia, Pontus, Lazistan, Kurdistan & Alexandretta Sanjak on the east, a Turkey that has lost an entire generation in WWII, on top of the previous losses suffered during WWI, is an ATL Turkey that will be limited to 30 - 35 million people maximum nowadays.
That being said, they'd still be a significant challenge, despite being much more on par with Greece, they'd still hold a 3:2 numerical advantage at the very least. The best way to neuter their significant demographic advantage would be a strategy similar to the Israeli one regarding their Arab neighbors, and if that's not possible due to the sheer amount of chaos it causes in the wider region, then a strategy similar to how France dealt with Germany thought the first half of the 20th century, the construction of strong fortification lines along the borders, alongside with the seizure and exploitation of the major resources that Turkey has at its disposal, would result in a manageable Turkey for Greece.
I think they can do it if they have the political leverage to do so.
And yes, Greece can intervene on the Suez Crisis post WWII, if such an action is deemed to be in it's best national interests, the scope of their involvement and the nature of actions that Greece will choose to undertake can be up for debate, but Greece post WWII, unless already involved/bogged down in another conflict, which I very much doubt it, can most definitely intervene in the Suez Crisis and its political leadership would more than agree to it, if union with Cyprus was on the table, in exchange for the assistance rendered by Greece to the Franco-British-Israeli (& maybe Spaniard) forces.