A successful Gallipoli seems to be a quite popular POD, although most relevant threads have concluded it's ASB. Nevertheless, I still have some questions on that...
But, let's take things from the start:
1. In order to have Greece joining the campaign, Constantine has to be out of the picture. The best POD on that is that George survives the assasination attempt of Schoinas in 1913. That way we have both the government and the crown on the Entente side from the beggining of the war. Otherwise, a coup is needed, but this is not certain if it succeds, since the crown had a lot of dedicated high rank officers, while the majority of the Greeks were seeing Constantine as a war hero.
2. Given the above, the next problem is Bulgaria. The Entente wanted both Greece and Bulgaria on her side, arranging concessions to both of them. Venizelos had agreed on Bulgaria getting Kavala after the war, while Greece was to get Ionia, but not Eastern Thrace, since the latter was on Russia's share. If things went like the initial Entente plan, Bulgaria would attack Eastern Thrace, while the greeks would participate in the Callipoli campaign. Otherwise, many believe that Bulgaria was never intenting joining the Entente, and was only buying time. In that case i can see the bulk of Greek forces staying in Macedonia, while a corps will be participating in Callipoli.
3. Some insist that the Ottoman defence in Callipoli was not possible to break. I object, since if Greece participated, there would be three crucial differences than OTL: a) The Greek troops participating would not just add manpower to the campaign, but also a quality contribution: Greeks had already fought two wars (Balkan I & II), so they were veterans, and acustomed to fight against machine guns and modern artillery in a mountainous terrain, and they had proven they could afford all the casualties necesary, b) the latter aplies also for the Greek Navy, which means that a Dardanelles entry would be more insisting, c) the Greek Navy had the experience of cooperating with air forces, and if that knowledge was materialised by the British too, thing at the Dardanelles could be also different.
4. Nevertheless, even if the Callipoli campaign succeded, if Bulgaria is not on Entente's side, I' m almost sure she would join the CP and the Ottoman Empire in the event of British and Greek troops in Eastern Thrace. In that case large reinforcements by the British and French would be needed in order to maintain a Thracian front, while more reinforcements would be necesary for the Macedonian front in order to maintain Greek and Serbian defence in Macedonia. Of course, there's the point of OE surrendering if Constantinople falls fast, and in that case the Russians could move troops in Thrace, and even keeping Bulgaria out of the war.