Between the Turkish entry in February and the wars end in early May, there was a narrow window during which the Turks could have managed to get boots on the ground in at least some of the Aegean Islands still occupied by the Germans sinced the botched British attempt to aid the Italian forces who had switched sides in '44.
Even though it's quite likely, even if they get lucky in not getting repelled at the beaches, that there's not enough time to actually defeat the German garrisons defending them. However, they don't have to - they merely have to get the foot in the door; once Hitler kicks the bucket and Germany surrenders, those forces will surrender as well.
So, let's say they do so. Now what? Can they leverage keeping them, by arguing the Italians didn't uphold the 1912 treaty with the Ottomans that stipulated they were to eventually return the islands?
That had been overturned by both Sevres and Lausanne. There is a number of factors at play here. So our scenario is that the Turks attack on their own the Dodecanese islands and the Germans who where resisting Greek and British attacks against the islands surrender to the rather weak forces the Turks can land instead. For good measure the Turks did the operation on their own without Greek and British involvement. (the Greek navy alone in 1945 is way stronger than the Turkish, with the single possible exception of Yavuz) Then for good measure when the inevitable argument of "ok you freed the islands lets have a referendum on their future, now" comes, Turkey refuses outright because if they accept they lose it so overwhelmingly it isn't even fun.
It doesn't look very well for Turkey to put it bluntly with the Western public or for that matter western governments. Starts with opportunism, the accusations are already in the air after all, moves to rumours/accusations of collusion with the Germans and from there straight to accusations of violating the UN charter on the right of self determination. Now before we even get to the eventual creation of NATO there is the matter of the straits crisis in 1946. This could play in one of the following ways
1. The Soviets still press on but the West makes help conditional on leaving the Dodecanese. If Turkey fails to budge it is left to the Soviets tender mercies. If it budges which is more likely it has seriously affected Turkish opinion of the west. Abolition of the single-party state after 1949 was largely due to Western pressure. Also the British argument in favour of admitting Turkey only in the Baghdad pact and not NATO likely gets way more support, ironically one of the factors against this OTL was Greek support for Turkish entry, quite possibly the British have their way. When the equivalent of the 1960 coup come it's quite likely to turn into Nasserism, with Alparslan Turkes playing Turkish Nasser.
2. The Soviets see an opportunity and the Turks turn to the Soviets once more. Stalin backs the Turkish claim on the Dodecanese and does not make any territorial claims on Turkey, if Turkey is a Soviet ally why bother? This is in effect a return to 1920-1935 or so were the Soviets outright backed Turkey against Greece in 1920-22 and then had very friendly relations with them all the way up to the run to WW2. Turkey doesn't turn communist. It instead remains a single party state under Inonu, ostensibly unaligned but for every practical purpose in the Soviet camp. A role model for the Arab nationalists here...
3. The West shallows their pride/dislike and back Turkey over the straits even though it refused to budge on the Dodecanese. Things originally remain close to OTL... but Washington and London will very much remember. Less economic aid to Turkey TTL likely and just like in 1 there is a good chance Western aligned Turkey is left outside NATO.
And in all three scenarios you have most likely seen Cyprus uniting with Greece, in 1 and particularly 3 this could involve an exchange of populations between the Greeks of Rhodes and Turkish-Cypriots, a scenario whose plausibility the US looked into even in OTL, here if Rhodes is already Turkish it seems much more practical. Also in all three scenarios you are likely seeing Turkey out of NATO and increasingly drifting out of the Western orbit, in 2 it did not enter the Western orbit in the first place...
