It might be interesting if Franz Ferdinand was not seriously injured, but Sophie was killed in the assassination attempt. Given the nature of his relationship with her that very likely would send FF into a vengeful rage, so we might see Austria-Hungary move quickly decisively against the Serbs, rather than dithering for a month and letting the initial shock and anger over the killing die down.
Russia would not like losing the Serbs, but I think an immediate attack and quick Austrian victory would present Russia with a fait accompli; certainly the Tsar is not going to be estatic about encouraging regicides. If Austria had acted quickly Russia might well have decided to give up Serbia, and shift to some other Balkan state as their favored proxy; Bulgaria seems the most likely choice, especially since the Bulgars can take Macedonia while Serbia is being crushed.
On a semi-related note, I am a little fuzzy on why Russia stopped sponsoring Bulgaria in favor of Serbia, given that Russia's main interest in the Balkans is Constantinople and the straits, which Bulgaria is in a much better position to threaten than Serbia.
Chengar
Historically Bulgaria was Russia's main proxy in the region but this ended during the Balkan wars in 1912-13. Fairly complex but both sides made a mess of their diplomacy. Due to the geography Bulgaria did the bulk of the fighting. This included getting greedy after early successes and making a grab for Constantinople. Partly due to this and the geographical layout Serbia ending up occupying the bulk of the Macedonian lands the Bulgarians wanted. [Some suggestion when I read a book about this that the population identified more with Bulgaria than the other powers]. There was a pre-war agreement that would have given Bulgaria a proportion of those lands. However Serbia's designs on Albania and getting a coastline were blocked by Austria at the great power conference on resolving the issue so it was less willing to give back any territory. Furthermore Bulgaria was also getting greedy in the SW, trying to make a claim for Salonika, which Greece had occupied with a small Bulgarian force also present. Hence Bulgaria suffered a lot of losses for less gains than it thought it deserved. Also Rumania pressurised it out of some land in the north, to balance Bulgarian gains, while the Bulgarian army was tied up with the Turks.
The immediate result of this was that Bulgaria and Serbia/Greece found themselves on opposite sides in the 2nd Balkan War. A poorly organised attack was largely called off at the last minute, giving Bulgaria the worst of both worlds in having no success but the blame for the 2nd war. It was already struggling to hold those two when Turkey and Rumania ploughed in and really carved the country up.
This affected relations between Russia and Bulgaria because the Bulgarians thought they had an agreement for Russian support and were dissatisfied with the diplomatic support they did get. I get the impression that Bulgaria really made a pigs-ear of its diplomacy in this period. If it hadn't have antagonised Greece by staking a claim for Salonika it might well have been able to handle Serbia on its own or pressurise it into giving up at least some of the disputed lands. Instead of losing further land to the Turks, who got back the Adrianople area and Rumania. It also felt bitter about events, especially to Serbia, its main opponent and Russia, which it felt had deserted it.
With relations between Russia and Bulgaria poisoned Russia was left with Serbia as its only real client/ally in the region, which may be one reason it was so determined to support Serbia against Austria.
Steve