The Key is to get a war in the 1840's, a time when Russia was militarily backwards compared to the rest of Europe and hadn't started modernizing yet. Even by the time of the Crimean War Russia was still mostly relying on old muskets and doctrine from Napoleonic Times. If Austria can use Industrial Infrastructure and war-making abilities against Russia it could conceivably win a war with Limited Objectives against Russia because Russia was notoriously slow to mobilize, a quick victory using railroads to move troops would allow for a limited objective war to be carried out and the Russians to be forced to the peace table.
The Problem of course is that it can only be pulled off once before Russia begins to modernize due to the shock of a lost war.
Another Problem is the lack of industrial infrastructure in Eastern Europe in the 1840's. You could concievably move troops via railroad into Congress Poland, but not much further than that. . .