Hmmm? I think I see the mistake. There were two conflicts, not one, for all that they're closely related. In 1792, there was the Russo-Polish war, in which the Russians invaded in support of the Targowica Confederacy, and in which the king's nephew Józef Poniatowski led the army with Kościuszko, among others. In this war, the King signed a peace treaty, and the war came to an abrupt halt (though there was talk of Józef taking the King, bringing him to the camp under "protection," and continuing the war). Kościuszko was never captured in this campaign, and served only as a military leader. Soon after this, the Second Partition (1793) reduced Poland further, in direct violation of Russian promises. In 1794, the Russians and Prussians together decided to demobilize the Polish military and integrate it into their own, for their own protection. This led directly to the Kościuszko Uprising of 1794, in which he took a lead role, was captured, and was sent to St. Petersburg. The uprising, however, continued even after that; it's just that his successors (Wawrzecki militarily and Zajączek politically; the king himself was effectively irrelevant at this point) weren't up to the task of keeping the fractious rebel fractions together politically, and in either case, were compelled to surrender in November after military defeats. Two weeks later, the King was forced by the Russians to leave Warsaw for St. Petersburg himself, and within the year, Poland ceased to exist. There was no peace, because as far as Russian and Prussia were concerned, it wasn't a war to begin with; it was just putting down some rebs.
If Kościuszko hadn't been captured in the 1794 uprising, he would have been free to prosecute the war with the king's unlimited support (insofar as that meant anything), because it's very unlikely the king would have signed a second treaty after what happened the year before. If he and Józef Poniatowski had kidnapped the king and continued the war in 1792, it's more likely that they would have done it in the king's name (protecting him from the vipers of the Targowica Confederacy who forced him into it under duress, or some line like that), or else made Józef himself the new king due to his blood ties and the fact that the present king had no legal issue, rather than declaring a republic. In either of those two cases, with complete control over the Crown and powers of government, they probably would have liberated the peasantry and turned it into a national war of liberation as per both of their wishes, at which point it would probably just go right into a replay of the Kościuszko Uprising and its ultimate outcome. Even if they and the Russians want to keep the Prussians out, it's unlikely the Poles in Greater Poland would desire that, and an uprising there would make it a Prussian interest as well (not that they even need an excuse). The only way they can survive is to keep winning long enough for Napoleon to become a bigger threat than the Polish side-show, and even that will only last so long as Napoleon remains a threat. For the same reasons they historically did, it's likely Poland would still side with Napoleon, and if he loses, Poland still loses its existence. If they stay neutral or side with the Coalitions (say, after Russia and Prussia are compelled to side with Napoleon, but before Napoleon invades Russia), then they probably still get eaten in the end; if it's not as the price for Prussia and Russia to support Napoleon at Tilsit, then for the price for those two powers to accept peace at the Congress of Vienna during the inevitable Poland-Saxony crisis or its equivalent. Remember, the historical resolution of the Congress of Vienna called for an "independent" Poland with the Russian Tsar as sovereign, and we all know how long that unstable situation lasted. Sadly, I think 1792 was simply too little, too late; it would have taken a miracle, and not a small one, to preserve an independent Poland against both Russian and Prussian ambitions.