The Russian fleet's performance against the Japanese was pitiful, and somehow they are supposed to do better against the premier naval fleet on the face of the planet? They nearly started a war with the British in 1904 from sheer incompetence.
Yeah, considering the Russians managed the Dogger Bank incident when they were in the wrong ocean (and almost the wrong hemisphere), fighting against the UK with Germany sending out ships too will almost certainly result in the Russians sinking the first German fleet they come across...
Also, depending on when this war starts, there remains the massively pressing issue of nitrate supplies. Anything before about 1910 and the Germans are starved of ammonia and unable to produce explosives on a large enough scale to hold back the Entente more than a year. That's just feeding the war machine. Feeding the population would also be a crisis. German agriculture was responsible for about 40% of the world's nitrate consumption before the war, and Entente blockades OTL cut them off completely. Even though Russia could help a bit, there's only so much you can do when fertilizer supplies collapse (as Austria-Hungary saw OTL, where per-area production fell by 30-40%). While AH would probably fall before the German munitions situation went truly sideways, the efforts to feed a war ravaged Austria (which 'German Liberation and Unity' propaganda likely to exist in such a world would pretty much require) would just make the situation worse. The Western Front would just have to hold out long enough for Germany to either run out of munitions or run out of food, and neither of those would take long. (Though obviously a desperate Germany launching a spring offensive type 11th hour assault and knocking France out is quite plausible.)
If we're going for a 1914 war around Serbia and Archduke Ferdinand (killing more than a few butterflies)... the only way I could see Austria possibly doing that is if the Italians are securely on the Entente side (and I mean
securely). You don't give grandiose ultimatums when you're surrounded by enemies (unless you're crazy), and by that. Otherwise it just becomes a particularly loud version of the Moroccan crises.
Also, I see a lot of talk about French and German investment, but very little about the UK. Considering the British had very rocky relations with Russia for decades beforehand, and their views on the importance of preventing a European hegemony to threaten them, I think the UK would almost certainly provide massive investments in Austria-Hungary (and to a lesser degree the Ottomans and Bulgaria) to help hold back the Russians.
I still see almost no way for Austria-Hungary to make it through the war in one peace (and low odds on political stability for the Ottomans too), but an early war can see the Russian-German alliance lose the war, while the later one delays the war the more a war starting relies on giving the Entente more members (be it Italy or the Americans) in order for them to see the war as at all winnable. To be honest, I think a Russian alliance would see the Kaiser acting a lot more aggressive in earlier crises, dragging Germany into an almost certainly lost war, buoyed by overconfidence at having mighty Russia to back them up.