Depends on how they win. If they perform as badly as OTL but win through Japanese bankruptcy, they won't lose face or South Sakhalin but they will by no means be able to project more towards the Far East, not while their finances stay in awful and the Poles keep agitating. Mind that Korea's on the other side of Eurasia and, in 1900, had a population of around 12 million, which was about 10% of Russia's total population. Administering that will not be cheap (it would, however, make the Trans-Siberia Railroad even more important than OTL) and Korea's got a history of not being receptive to foreign occupation (the double Polish-Korean quagmires, could be, with the UK and Japan funding rebels on both sides of the empire).
In any case, it will likely keep the Russians assured of their superiority and lessen the immediate desire for reform. Which isn't good as the military reforms after the Russo-Japanese debacle kept Russia's army competitive with the rest of Europe's. Russia's not going to suffer the same amount of unrest immediately but Germany could potentially roll over Russia and gut it before it gets enough of a wake up call to reform in an ATL WWI.