It probably wouldn't change much for the early events, considering the battles Jotaro participated in weren't ones where time stop would've played a major role beyond giving him an edge in escaping against Rubber Soul. In Egypt, it'd make Jotaro be able to defeat Daniel J. D'arby far easier considering D'arby would have little way of being able to prove Jotaro was cheating and the same would probably apply when facing Telence. Things mainly change when it comes to facing DIO as Polnareff would be able to immediately tell DIO had the same ability as Star Platinum, meaning Kakyoin wouldn't have to sacrifice himself, Jotaro would be able to take on DIO easier due to having improved his time stops and Part 3 concludes with a far easier battle (Avdol and Iggy still die though due to Jotaro being preoccupied with Telence).
Moving onto Part 4, there's little Jotaro himself could change. Kakyoin's survival, however, changes a lot as he'd likely volunteer to help out in Morioh, perhaps replacing the Speedwagon agent giving Jotaro information before fully getting involved once Joseph arrived. Kakyoin would relate to Josuke quite a lot due to how their Stands would've made relating to others difficult and perhaps act as a mentor figure to him and Koichi. Of course, he'd also go on the Milf hunt due to Josuke's mom. A long range Stand like Hierophant Green would also allow the group to track down Kira before he could switch faces with Kosaku, leading to Part 4's plot ending a lot earlier.
This could open up the possibility for Kakyoin being present in Part 5 if Polnareff gets in touch with him. If so, the pair of them may defeat Diavolo at the Collosseum due to Hierophant's range and Chariot's piercing strength proving something Diavolo couldn't counter with Epitaph unless fate asspulls him a way out of things. Assuming Kakyoin survives or doesn't participate, then the Speedwagon foundation would reach out for him in Part 6 and his involvement may be enough for Jotaro to kill Pucci, seeing as how Hierophant Green's range may prevent Pucci's knife tactic from working.