Well if it happens, the American and British forces will stuck in a stalemate or more possibly, get wiped out. American and British forces may score some victories because of the surprise attack, but when Soviet forces reorganize themselfes, American and British troops already lost.
Soviets division in Europe (1945) outnumber the Western Allied forces by 3:1 ratio. And their troop isn't poorly equipped anymore. Soviet troops that storm Berlin mainly use PPsH and PPS. Also T34-85 and IS2.
Also, the American and British already discharged their troops and send them home. Imagine the public anger if they must took them again to fight the Soviets. And the Americans haven't even beat Japan yet.
My speculation is, for the first month, the Western Allies may reach Berlin, or even take it. But when the Soviets reorganized, they counterattacked and put the American and British forces to the original line. After this the British may propose peace or ceasefire.
The Soviets most likely won't accept the peace and continue to push to France. The American and British forces retreat to British Isles from Calais. And the atomic bomb got redeployed to Europe.
That's my best speculation for Operation Unthinkable. I don't really know what will happen after the Soviets "liberated" France. Maybe a mushroom cloud in Moscow, maybe a Communist State of Britain..