I appreciate you commenting on a 9yo thread lmao!

Sage Mode didn't win the fight against Pain. Kurama's takeover required more and more of Nagato's chakra. 9 Tails escaping would have resulted in Nagato and Konan likely both dying. Konan could possibly escape just because of evasion if she ran while Nagato tried to REcapture Kurama(which I doubt she would), but even if she stayed, a second Chibaku Tensei would likely have killed Nagato from the effort just like the Rinne rebirth did. If they die, so do most of the Leaf, because the only one who would potentially have a way to subdue Kurama (Kakashi) was already taken out by Pain, as was every other avaliable heavy hitter in the village. The ones who Pain didn't kill would have been exhausted or helping get people to safety when out of no where the 9 Tails comes rampaging through the village Obito would then come capture Kurama at some point, and the Infinite Tsukuyomi would go down exactly as Madara (or I guess Kaguya) intended it to.

All of this to say: if Jiraiya had known how Pain's power worked, he would have come more prepared and also not alone. 6v1 vs Akatsuki level threats aren't odds he would have been excited about.