If Greece went Communist, would a Greco-Turkish War be inevitable?

So basically I was reading about the Greek Communists claimed government and got to thinking about the butterflies resulting from a Red Greece. I assume, that the US would fund the shit out of Turkey and lead to a militarized border between Turkey and Greece. So if say, the Cyprus conflict breaks out like in OTL, (not exactly the same obviously) would war break out between a US supported Turkey and a Soviet backed Greece?
 
No because that would be a war between a Nato member and a (probable) member of the Warsaw Pact. This would not happen over a Cyprus that Nato would set up as a haven for non Communist Greeks, with the full backing of the Orthodox Church in Cyprus. Britain will see the island partitioned before independence rather than risk a Communist Greece getting a foothold by stirring up intercommunal strife.
 
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