We'll assume the war breaks out in 1970, as an escalation of the border clashes in 1969. It would almost certainly begin with a Soviet pre-emptive strike on Chinese air bases and missile bases and nuclear weapons facilities. The question is whether this attack would prevent any Chinese retaliation.
Maybe it would not... China was developing its first IRBM, which deployed in 1971, and had range to reach Moscow (barely?). China also had some bombers with the necessary range and payload.
Supposing China retaliates by destroying Moscow, and decapitates the USSR. (Or would the Soviet leaders be in hiding somewhere else until they were sure the Chinese threat had been scotched?) China might also hit several other cities, especially in Soviet Asia. This in turn might provoke a general strike by Soviet forces on China, to kill the leadership and smash up the PRC state. The Soviets had lots of bombs, and would use them freely. Every major city in China would be destroyed, leaving the country in anarchy.
In those conditions, the RoC could move onto the mainland with a substantial army. The RoC holds islands that are just off the coast (Quemoy and Matsu). Moving ashore from there would be fairly easy. If the US provided logistical support, the RoC could occupy a fairly large region. If the population in that region accepted RoC rule, it might be possible for the RoC to "pyramid" its conquests up to the whole of China. China would need large scale relief for the damage of Soviet bombing; if this aid was funneled through the RoC, that would give the RoC a leg up.
OTOH - if the Sino-Soviet war stayed "conventional", the RoC would not have much of a look-in. As long as the PRC held together, its forces would be enough that it could defeat any RoC invasion with a small portion. Though if the PRC was badly defeated, with the loss of Beijing and break-up of the central government, the RoC might be able to gain some ground.