I find it very hard to see how such a war would break out in the first place. It would imply that Russia and Austria-Hungary found some way of balancing their interests in the Balkans (probably to the detriment of the Ottomans, so they might well be inclined to join the other side). That removes the biggest European flashpoint, and the one that triggered war IOTL.
Without a Russian military convention, and knowing Germany's eastern flank is covered, France is unlikelky to chance a war, and Germany has no real reason to, given diplomacy has tamed the cauchemar des alliances.
With Russia having managed to lay to rest the spectre of a Russo-Austrian confrontation, its primary conflict is with Britain, so that part works. But you would still need to lay to rest Franco-British differences and encourage the resulting two-power entente sufficiently to choose to go to war with Germany and Russia. I can't see London or Paris (the most hesitant of the August sleepwalkers) choosing to do that.
Of course, I also find it hard to see how a Berlin-Vienna-St Petersburg coalition can continue in the first place. It would require either an external threat felt equally by all (a far more assertive and arrogant Britain?) or a triumph of skilful diplomacy over geopolitics. Assuming the endgame is an Austro-Russian partition of the Ottoman corpse, I wonder what's keeping Germany in the club. The threat of a Franco-Russian entente would be far removed, given how much France is invested in protecting the Mediterranean (the last thing they want is another fleet in there). Would that make Germany a promising candidate for 'turning', the target of diplomatic blandishments by London and Paris? It would be an amusing scenario, Germany (with no obvious potential gains and no interest in expanding territorially to the west) suddenly and brusquely telling its loyal allies to sod off and reaping the resulting peace dividend (or even carving the choicest cuts out of the Russian carcass). Bismarck was that kind of magnificent arsehole, but I don't think there's that kind of sang-froid in Wilhelmine Berlin.