Did the demonstration of atomic weapons prevent a possible occupied red Tokyo?

No. While obviously strong, the Red Army stood no chance of invading Honshu. Simply put, they didn't have the sealift capabilities to pull it off.

As the Pacific War drew to a close, the Soviets did invade the Kuril Islands. They managed to eventually land about 15000 troops there, who were faced with defeating 80000 Japanese troops. Unsurprisingly, they were having their hats handed to them when the war ended... and thus took possession of the islands.

Unlike the US, who had specialized designs specifically for troop transport and amphibious landings, the Soviet Pacific Fleet had, in comparison, nothing. They had a handful of landing craft given them by the US, but other than that they used minesweepers, destroyers, torpedo boats, and generic freighters to move their men to the Kurils. They were then unable to reinforce them with any sort of speed. It takes very little imagination to see that invasion being defeated if the war had gone on longer.

Invading Hokkaido, on the other hand, would have required many, many times more men and materiel than the Kuril invasion. And while the Red Army was a force to be reckoned with, it could not walk on water.

Heck, the US was less than sanguine about invading Tokyo. They would do so if needed, and fully expected to win, but at grievous cost... and they could move their troops in immense quantities with heavy air and sea support.

One can say, I think, that the US timing on the atomic bombings (as soon as possible after Potsdam ended) was in part due to the hope that they thought they might cause the Japanese to surrender before the Soviets entered the war, thus denying Moscow the concessions that were promised at Yalta should they enter it. This is reflected in some of the discussions at the top levels, in any case.

One can also say, without any doubt, that the bombing of Hiroshima did speed up the Soviets' campaign against Japan, because Stalin feared that they would indeed surrender quickly. We know that after a day of moping after Hiroshima, he told his marshals to push up the schedule as soon as they could, and the invasion took place at midnight (Transbaikal time) August 8/9.

But I don't think one can say that the atomic bombs prevented the Soviets from getting a foothold on home islands. Preparing a serious amphibious invasion of that sort took time. There is reason to believe that the Japanese would have surrendered prior to an American invasion (scheduled November 1st) even if the atomic bombs or the Soviet invasion had not happened. (This is what the US Strategic Bombing Survey concluded in 1946, and what some other scholars have concluded since.)

To imagine the Soviets invading the home Japanese islands would be to extend the war's timeline by many, many months — well into 1946. If that had happened it would have been a fairly desperate situation in any case.