A delayed and possibly constitutional Russian revolution

Would defeating the Ottoman Empire prevent the Russian Revolution?

No, but it might delay it until the 1920s and make a constitutional outcome more plausible.

The answer separates structural Russian political problems from the wartime crisis that made 1917 possible. A victorious, fed, and demobilized army would change the balance between the monarchy, moderate reformers, and revolutionaries. A later political confrontation might seek a constitutional monarchy, although Nicholas II could resist it. Gallipoli success changes the timing and balance of forces in this scenario rather than removing the social and political causes of unrest.