Russia did not have an Austria only mobilization plan, they only had a full mobilization plan. In this way, they are like the Germans. However, the Russians had two war plans, both which started with troops near the same location. If the Germans attacked hard, they would retreat, rapidly pulling forces out of Poland. As the supplies lines shortened, they would counter attack and stabilize the front at some point. Basically trading land and men for time, in classic Russian tradition. The Russian line would stabilize at or west of a Riga/Minsk line.
The second plan assumed the Germans would attack France first. The Russians would attack East Prussia and Galacia. After these areas were secured, there would be a followup drive into the heart of Germany. This was the plan executed. If Tsar Nicholas changed the plan at the last moment, it would likely cause logistical chaos. The overstretched Russian rail system would need to move one armies south to attack A-H. It is possible the logistical chaos would make the Russians move even slower than OTL. Is the Tsar order to attack as the forces arrived or does he want the reinforcing say 2nd Army to arrive before the attack is launched?
Even if the Tsar order forces to attack as they arrived, i don't expect them to be a major help in 1914. The Russians are facing a limited weather window, that will close after a few months. A best case for the Russians is they get most of A-H north of the Carpathians. A medium case is the 2nd Army has little effect, and arrives too late. A bad case is Tsar Nicholas delays the initial attack until the 2nd Army arrives or the change in orders delays the attack into A-H by weeks, giving the A-H more time to organize a defense. In any case, the additional Army will not be decisive in the first year of the war against A-H.
Unless the offensive against A-H is a bust, Italy still joins the Entente. The German general staff does not need to move the 3 corps to help the 8th German Army. With 3 or more extra corp and less panic pressure to move troops east, the Germans do better in the west, but do not take Paris. The Germans likely either hold the Marne or take a lot more of the Channel coast, depending on where the extra corps are used. I am not familiar enough with the details of the western front to know where they would have been used.
Now everything is different if say 4 years before the war, the Russian High commands draws up an A-H first mobilization and war plan. This POD would have a good chance of decisively breaking the A-H lines and winning the war quickly. Basically, i doubt the Russians ability to move 200,000 troops from one area to another without causing chaos. I also think it likely that if the Tsar had chosen this path, a few weeks later, he would have changed his mind because France was screaming at him about not helping them. I can see the 2nd Army almost being ready to attack from Lublin, only to be order to rush back to their original positions to attack Prussia.
http://www.ww1-world-war-one.info/ww1-information-History-Eastern-Front-War-Plans.htm This is a basic summary, i can't find maps to the plans quickly.