In this scenario, Jiraiya still loses an arm, still gives Fukasaku a code and sinks to the bottom of a lake... then at the last second, he's saved.
Let's make it something like, a toad Kuchiyose's in and saves him.
The rest plays out more or less the same, with minor nuances:
- The severity of Jiraiya's wounds has left him in a bit of a coma, he might not survive (which motivates Naruto into going to Myoboku to become the next Sen'nin, which isn't as strong a motivation as Jiraiya full-on dying, but still).
- Jiraiya's code still needs translation from Naruto, because the former is out of commission and can't offer the information himself.
- Pain thinks Jiraiya's dead, and proceeds as if this were the case.
Now, while Naruto is training, the day before Pain arrives, Jiraiya wakes up. He tells Tsunade, Kakashi, the ANBU, Ibiki, Shizune, Shikamaru, everyone relevant the full picture: he thinks that the Six Paths are corpses that are being controlled, and the real one is elsewhere.
Then, three days later: Pain invades Konoha.
1. Would Jiraiya being in the village - even if one-armed - give the shinobi there (who're unknowingly buying time till Naruto arrives) a bit more of a fighting chance? He can't go into Sage Mode, because Fukasaku and Shima are training Naruto, so let's just give him the abilities he showed in Part 1. Would him being there with the shinobi help, from a military POV? Like, would Kakashi still have died, for example? Would more Paths have been defeated before Deva did that village-destroying Shinra Tensei?
2. Would the intel he provides 1 day in advance be enough to defeat Pain before Naruto arrives? Would it help? Would they have found Nagato sooner? Or would things have played out more or less as they did in the original manga, regardless of Jiraiya's presence?
3. Would Jiraiya be able to reach Nagato emotionally or get him to change his ways? Or was Naruto the only one who could do that?
Trying to see if Jiraiya having been there would've made things better or worse.