I am curious as to how this could happen. From what I know of the Frist Balkan War (admittedly not so much), the Balkan allies had a pretty big advantage over the Ottomans. Maybe the Ottomans accept some kind of Cypress type deal allowing Italy to control Libya while nominally retaining it in the empire, meaning they look weak to the Balkan allies but also have their most modern forces in Europe when the Balkan war starts, instead of on the Egyptian border?
I have a hard time seeing the Ottomans gaining much territorially. However, gaining war reparations could potentially be quite the financial boon.
An Ottoman victory in this war and an avoiding of the domination of Enver Pasha of Ottoman politics could have REALLY interesting impacts on WW1 though.
It's often forgotten now, but the Young Turks' constitutionalism was initially well received inside and outside the Empire, giving it more cred with liberals than many of the Balkan monarchies or Russian Tsarism. When alt-WW1 starts in this scenario, the Ottomans haven't been so deeply humiliated and so look like a more useful ally and will have more friends in France, Britain and the US.
Also, WW1 is one scenario where I can see the Ottomans being able to regain territory from "Christian" states. So even if the Ottomans don't regain anything at first, if they can survive WW1 and join at the right price, they're in a good position to regain territory.
fasquardon
The Ottoman Strategy was so flawed that the Balkan States had the advantage to overrun and crush the pocket forces within a month. Then there is also Hasan Tahsin Pasha surrendering Saloniki without a fight.
The war would develop with losses in the beginning. But as soon as the Anatolian Forces are ready, the offensive on Bulgaria can start which kicks Bulgaria out of war.
Another disadvantage was the Greek Navy in the Aegean. If the Ottoman Navy caught the Averoff early on the Ottomabs would be somewhat in better position.