In the long run very little, in the short run, lots of Russians don't die. Even if the 2nd Pacific Squadron managed to get to Vladivostok there's little they could do. They would either be blockaded in the port or just act as a fleet in being.
They would need weeks if not months of refit and repair, the fleet commander would need to be replaced, the poor chap had more than a few nervous breakdowns on the voyage (Micro-manager + incompetent crews = FFFFFFFFFFFUUUUUUUUUUUU........) as well as discipline boards to deal with the various mutinies etc.
Also apart from the four Borodino's the Russian ships were totally inferior to their Japanese counterparts and the Borodino class is usually pointed at when someone wants a bad example of a pre-dreadnought.
By Tshshima the Russians had basically lost the war, Port Arthur had been overrun and the fleet there destroyed or interned whilst in Manchuria the Russian armies had been routed but more were on the way. The Russian fleet was basically a poorly trained mob that never really stood a chance and if they did reach Vladivostok they'd need so long to refit that the war would end before they were ready.