The end date of the Soviet-Japanese Border War oddly coincides with the beginning date of the Soviet invasion on Poland in 1939. Was the end date of the Soviet-Japanese Border War the direct reason of starting the Soviet invasion on Poland on 17th of September 1939?
(In other words if the Japanese army had stood longer, then the Soviet invasion on Poland would have been delayed and might have had an influence on how the Invasion on Poland moved.)
The question has it backwards: It was the planned invasion of Poland that caused the peace agreement to happen, not visa versa.
This war was never officially declared, and it took place on the border of Mongolia and Manchukuo (a Japanese puppet state) because of the disagreement about the location of the border. Militarily, the Soviets (and Mongolians) prevailed. But they had to agree on cease fire because their planned invasion to Poland was more important than the Mongolian - Manchukuo border dispute. The ceasefire was signed 2 days before the attack on Poland.
The Molotov Ribbentrop pact, which made the invasion of Poland possible and feasible was signed on Aug 23, 1939, while the decisive Soviet offence in Mongolia began on August 20. So the Soviets understood that they were winning in Mongolia at the time the decision to invade Poland was made. This Soviet-German pact was a sudden opportunity for the Soviets, and it happened in the middle of a less important conflict in Mongolia. So they did everything to end this minor conflict.
In April 13, 1941 a Soviet-Japanese neutrality pact was signed (it left the question of Mongolian-Manchukuo border open).
The agreement on the border was only signed in May 1942, and Soviets essentially yielded to the Japanese demands (despite their military victory). The reason is of course that Soviets had much more important things to care about in 1942.
I conclude that the causal relation between the attack on Poland and Soviet-Japanese ceasefire was just the opposite to your suggestion. The Soviets had to sign a ceasefire, because they were in position to do this (they prevalied militarily), and because the invasion of Poland had much higher priority.
(The dates of the treaties are based on Russian Wikipedia).
Remark: The Soviets were fighting the Kuantung army in this war. The Kuantung Army was formally a part of the Japanese Imperial forces, however it was not completely controlled by the central government. According to the (English) Wikipedia, the whole creation of the Manchukuo state was an initiative of the Kwantung army, not of the Japanese government. Eventually the Japanese government approved it.
In other words if the Japanese army had stood longer, then the Soviet invasion on Poland would have been delayed and might have had an influence on how the Invasion on Poland moved
I would say the end of the Khalkhin-Gol battle and the Soviet entry into former Poland's territories was just a coincidence. Why?
There was nothing to influence on September, 17th, 1939 except the German troops' proximity to Moscow, since Poland had been already defeated
I know, in present day Poland's historiography there are widely accepted statements, that Poland was defeated by the double assault from Germany and the USSR. And had it not been a Soviet "invasion", Poland would have successfully repealed the German assault, since the Germans were starting to experience fuel shortages etc. (this particular "theory" was promoted by Polish historians according to Suvorov-Rezun, he mentioned this in one of his works), but these "theories" are questionable at the very least.
There was no functional government in Poland on Sep. 17th, an assertion which can be found in various sources like Tippelskirch's History of WW2 (in Russian), who stated that the government fled on Sep. 16th or Liddell Hart, who stated it fled on Sep. 18th., other authors (like Kacewicz G.) provided Sep. 17th as the date. For me it makes not much difference whether the Polish government was in Romania already at Sep. 17th or it was somewhere on the Romanian border ready to flee the next day.
The most astonishing thing about the "existence" of the Polish government on September, 17th is the anecdotal story about how the Soviets notified the Polish government about the necessity to enter the former Polish territory.
The Polish ambassador to Moscow Wacław Grzybowski refused to contact the Polish government on a request of Soviet Vice Foreign Minister Potemkin (in Russian, an extraction from the official journal of Vice People's Commissar of Foreign Affairs Potemkin regarding a discourse with Polish ambassador Grzybowski, sent to General Secretary of the VKP(b) Stalin, Sep. 17th, 1939):
the ambassador is refusing to report to the government about the Soviet note, which is trying to excuse this attack with arbitrary statements that Poland has been finally defeated by Germany and that the Polish government does not longer exist
When Potemkin replied that this was out of the ambassador's competence to decide whether to transfer a message from the Soviet government to the Polish one, Grzybowski said that the note should have been delivered via the Soviet embassy in Warsaw, Potemkin responded that there already had been no Soviet ambassador there. Then Grzybowski admitted, that he didn't have communication with the government but kept stating that the government was still in Poland and fully functional. After Potemkin's offer to use Soviet communication channels to deliver the note, the Polish ambassador responded that this (the suggested use of the Soviet channels or assistance) would have been repugnant to "the dignity of the Polish government". Long story short, Potemkin and Molotov were forced to sent a courier to the Polish embassy and to give the note to someone there (probably a doorkeeper) in return for a receipt before the Polish ambassador left Potemkin, lest he forbids the doorkeeper to sign the receipt.
Please note, that this story was taken from a book published by the International Democracy Fund, which had (the fund ceased activity just a couple of weeks ago) a strong affiliation with various Soros and the US government financed entities, so it would be hard to dismiss that as a "communist/Russian propaganda".
So in summary, the Soviet "invasion", the most likely, was motivated by the defeat of Poland, absence of anything, which could somehow impede the German reach further to east and the desire to keep the German troops as far from the main Russian territory as possible. The Barbarossa plan's success could have been much likely to happen, had not Stalin "invaded" Poland.
This opinion was pronounced by Winston Churchill:
On 1 October 1939, Winston Churchill—via the radio—stated:
... That the Russian armies should stand on this line was clearly necessary for the safety of Russia against the Nazi menace. At any rate, the line is there, and an Eastern Front has been created which Nazi Germany does not dare assail. When Herr von Ribbentrop was summoned to Moscow last week it was to learn the fact, and to accept the fact, that the Nazi designs upon the Baltic States and upon the Ukraine must come to a dead stop
