I believe it was possible for the 1913 coup to fail, but I don't know that its strictly necessary for it to fail for the Ottomans to remain neutral. Turkey faced obvious and serious threats, particularly from Russia, and lacked any obvious reasons to join the war. The decision to join in was made because the Pashas believed Germany would quickly win the war, because the British had seized Turkish warships on order in Britain and generally acted high-handedly, and because Enver Pasha in particular believed he could attack across the mountains into Russia quickly and seize a lot of territory by surprise.
Even then, the initial attack against Russia was carried out by the two German ships taken into the Turkish Navy without official orders. (They may or may not have had unofficial orders from Enver Pasha).
Note that the war was extremely unpopular in Turkey: there were riots once Turkey's entry into the war was announced, and an assassination attempt meant for Enver Pasha ended up killing some of his German advisors.
Note too that the Ottoman Empire in 1914 had declared themselves neutral in the war, rejecting initial German offers of territorial cessions (from Russia and Iran). Before the British seizure of their ships Talaat Pasha (one of the three Pashas) had even been reaching out to Britain to try to negotiate an alliance, though the intention wasn't to enter the war but rather to hedge bets by maintaining friendly relations with both sides.
Change Enver's calculations about the feasibility of crossing the Caucuses in winter and Turkey will want to wait until at least summer 1915 to join the war. But waiting that long gives the Pashas more opportunities to see the stalemate that had set in on the Western Front and the unlikelihood that the war would be a short one. More importantly, it would make it clear that the Russian army had neither collapsed nor stripped all troops from the Caucuses. The belief that the Russian army had collapsed was a major factor in convincing Istanbul to go ahead and declare war, but frankly even had the Russians collapsed they should have waited for summer before trying to push any serious kind of army across the mountains. In those circumstances, IMO, the Ottomans are unlikely to join the war at all- instead sitting it out as a somewhat pro-German neutral, much like Sweden.
TL;DR: the Ottoman decision to enter the war was based on a lot of dumb calculations about how easy it would be to beat the Russians and how safe it was to let a pair of German-manned ships sail around acting independently but with the full authority of the Turkish Navy. Put in somewhat smarter calculations and the decision likely never gets made.