All that a Japanese invasion of the USSR would have produced was more mass death, more human suffering, and might have resulted in communism becoming even more widespread throughout Asia.
From memory, a Quora user (I know, not the most reliable source) claimed that this scenario is commonly studied by the Chinese Armed Forces in modern times. They (the Red Chinese military) allegedly concluded that it would have been extremely difficult for the Soviets to win.
The Japanese made various estimates about how long it would have taken their army to conquer the Siberian "Maritime Province" (Primorye). The 1940 war plan estimated two months, the IJA General Staff estimated 6 to 8 weeks in 1941 (post-Barbarossa), and the timetable for an early version of the Kantokuen plan (22 divisions) worked out to 36 days (10 September to 15 October 1941).
According to
@Admiral Fischer, "Senshi Sosho" (Japan's official military history of the war) reports that this timeframe further shrank to only 21 days in the 29 July version of Kantokuen . I suspect that the main reason for this was because the Japanese army felt pressured to at least bring the first phase of their campaign to an end before the onset of winter, which would have severely hampered operations in Siberia and northern Manchuria. The Kantokuen plan's 'Primorye offensive' was also incrementally strengthened by an additional 3 divisions compared with the July 8th version (16 divisions in the first wave vs 13, with a central reserve of 5 divisions in both). A later version drawn up after July 31st increased this number again to 17 divisions with a further 5 divisions concentrated at Mutanchiang.
Personally, given the nature of the terrain, geographic constraints, and the size of the forces involved I consider the 3 week timetable very unlikely despite some militarily questionable plans by the Soviet army outlined below. The border area was hilly and heavily forested, and the Soviets constructed several layers of defensive positions, including concrete bunkers, ranging from approximately 1 to 12 kilometers in depth. There were gaps between their "fortified regions" but due to the number of Soviet military personnel (about 500,000 men along a frontage of 500 miles/800 km, most of whom were concentrated south of Lake Khanka) combat probably would have taken on an attritional character in most places. In my opinion, the most likely location for the Japanese to have broken through was at Iman (Dal'nerechensk) north of Lake Khanka, which would have turned the flank of the main Soviet army and created a gigantic Singapore or Bataan-type situation ending at Vladivostok.
The Soviets' insistence on an all-out defense of the border zone and actually planning an offensive toward Fujin and Baoqing probably wouldn't have helped their military situation either. The attack on Fujin by the 15th Army, in particular, would presumably have involved not one but two major river crossings (of the Amur and Sungari), to be accomplished by the 25th day of hostilities. The Soviets' apparent aversion to defense in depth and offensive designs in NE Manchuria may have left them vulnerable to a breakthrough in the event the Japanese pierced the 'crust' of their defensive belts and all Soviet reserves were already committed to the front.
According to the directives sent to the Soviet Far East forces on 16 March 1942, planned reinforcements totalled just four tank brigades, five artillery regiments, six guards mortar regiments, and five armored train divisions all together.
Historical Soviet transfers from the Far East to Europe between June 22 and December 1, 1941 amounted to 2,209 tanks, 122,000 men, 2,000 artillery pieces, 1,500 tractors, and nearly 12,000 automobiles (per Glantz and some Russian sources). Overall, the Russian historian Kirill Cherevko cites figures of 344,676 men, 2,286 tanks, 4,757 guns and mortars, 11,903 motor vehicles, and 77,929 horses transferred from the Far East prior to May 9, 1945, most of which logically would have been sent before early 1943.
In 1945, the Japanese estimated Far Eastern Russia's output of military hardware to be 400 aircraft, 150 tanks, 30 armored cars, and 550 artillery pieces; I don't know how well these numbers reflected the situation in 1941 (or even 1945), but the loss of even one year's production at those rates would not have been small.
The Soviets probably would have pressured the Allies to expand the Persian and White Sea routes, though the latter was quite dangerous due to German military activities.