The key question on this subject is what happens between Greece and Turkey. It’s been discussed before, which isn’t to say that it won’t be fun and constructive to talk about it again, and the problem with understanding the ramifications is that everything depends on how Greece and Turkey act, which in turn depends on the specifics of the scenario and on how you choose to interpret the available, and far from definitive, record.
Prior to the outbreak of the July Crisis, THE greatest point of tension was an escalating crisis between Greece and the Ottomans over control of the Agean islands. Indeed, from my reading it seems that contemporary opinion was that war between Greece and Turkey was all but guaranteed in the summer of 1914. To understand why we need to go back to the First Balkan War. In that conflict the Greek navy proved distinctly superior to the Ottoman forces and was able to dominate the Aegean. This complicated the Ottoman ability to reinforce their Balkan armies contributing to their deafest and, more importantly for the events of the summer of 1914 allowed Greek forces to seize the Aegean islands that had until then remained under Ottoman rule (think Lesbos, Chios, Lemnos, etc.). Most of these islands were subsequently assigned to be ceded to Greece by the London Ambassadors’ Conference. However, the Ottomans had withdrawn from the conference following the Young Turk coup in 1913 and consequently did not recognize the loss of the Aegean islands. So the Ottoman Empire was already seeking an opportunity to reclaim the islands in question. At the same time, tensions between Greece and Turkey were ratcheting up due to the Greek genocide then ongoing, particularly in Thrace and western Anatolia. In early June Greece issued an ultimatum over the matter and was seriously considering military action.
Until the July Crisis abruptly changed political priorities, the Greco-Turkish crisis was expected to come to a head with the delivery of the Ottoman dreadnoughts, for a number of reasons. Firstly, the First Balkan War showed the Ottoman government that it’s navy was insufficient to contest Greek control of the Aegean and protect Ottoman possessions, let alone allow a reconquest of the Aegean islands. However, Greek naval superiority would be completely overturned by the delivery of the new warships, whose presence would allow the Ottoman navy to be confident of defeating the Greek fleet in battle, or more likely force the Greeks to avoid contesting the Ottoman fleet. Either way, Greece would be forced to cede control of the Aegean to the Ottomans who would then be able to retake the islands. Secondly, Greece was considering military action over the Greek genocide which, for the reasons noted above, would realistically need to happen before the arrival of the Ottoman ships. Further, Greece had been negotiating with Serbia for military support in any future war with the Ottomans but had been unsuccessful. All of this meant there was a huge pressure for Something to happen in the summer of 1914, because the naval dynamic in the Aegean was about to be reversed. Either Greece would act before the Ottoman dreadnoughts arrived, or the Ottomans would act once they had them. There was also a time pressure on the Ottomans to seize the opportunity provided by their naval power as soon as they had it because while Greece did not atbthat point possess any warships which could equal or oppose the Ottoman dreadnoughts, it wouldn’t be too long before they did. Greece had responded to the Ottomans building Reşadiye by ordering a dreadnought, Salamis, from a German yard. Similarly, when the Ottomans purchased the Rio de Janeiro from Brazil Greece responded by contracting another dreadnought of their own, Vasilefs Konstantinos this time from a French yard. However, neither ship would be ready in time to counter the Ottoman ships in the short term. Indeed, Salamis wouldn’t be ready until mid-1915 and Vasilefs Konstantinos even later, leaving ample time for the Ottomans to make good on their naval superiority. As a stopgap measure Greece purchased two pre-dreadnoughts from the US, Kilkis and Lemnos, which IOTL arrived in Greece in late July (I couldn’t pin down the exact date they arrived, but Wikipedia lists July 22 as the commissioning date for both so we might as well use that.). Reşadiye was scheduled to be delivered to the Ottomans in very late July, IIRC she was scheduled for delivery and departure on July 21 before Britain delayed it. Sultan Osman I wasn’t quite that advanced as she was still undergoing sea trials, but both vessels’ crews were present and simply waiting to take possession, so we can expect both to arrive in very short order in late July-early August. Personally I don’t think Kilkis’ and Lemnos’ arrival does all that much to change the situation in the Aegean. While they certainly strengthen the Greek fleet, not only were they pre-dreadnoughts but they were designed as and intended to be second line warships against their own contemporaries. They can’t realistically stand against the Turkish battleships and so won’t meaningfully threaten the coming Ottoman advantage in the Aegean.
The last point to be considered, and one which was unknown to contemporary observers, was a plan by the then head of the Greek navy (whose name escapes me) to ambush the first Ottoman battleship as it transited the Ionian Sea with a torpedo boat floatilla. IIRC the proposal was to use the lack of hostilities between Greece and the Ottomans to get close enough to assure decisive hits on the battleship, even at the sacrifice of the torpedo boats. The head of the Greek navy suggested that he personally lead the ambush without official instruction so that the Greek government could publicly disavow his actions and, if he survived, execute him to avoid responsibility for the operation but buy time to act from a position of strength. Apparently the Greek Prime Minister, Venizelos, absolutely rejected the idea and forbid it. However, some of the sources indicate that the Greek admiral in question intended to donit anyway if the Ottomans looked set to take delivery of their ships. (I think there’s some talk about it in Admiral Kerr’s memoir, but I’ve definitely seen it elsewhere too).
So, this is all a very long way of saying that an earlier delivery of the Ottoman battleships changes the dynamic in the Aegean, potentially by a great deal. However, if we take the lesser initial change from OTL and say the ships arrive earlier than OTL but not so early that the situation is unrecognizable then war between Greece and Turkey in the spring and summer of 1914 is guaranteed.