In such a fanfiction, it could lead to some interesting plot twists and character developments. Maybe Goku's identity as Kakarot would be explored in a deeper and more complex way.
In my opinion, it's highly unlikely. Goku has mastered multiple forms and techniques that give him a wide range of powers. Saitama's one-punch style might not be effective against Goku's diverse skills and battle experience.
With his son Gohan, the relationship could be strained. Gohan has always looked up to Goku as a hero. But as Kakarot, Goku might push Gohan to be more like a traditional Saiyan, which could be too much for Gohan. Also, Vegeta's view of Goku would change. Vegeta has always seen Goku as a rival but also respects him. As Kakarot, Vegeta might see him more as a threat to the Saiyan way of life or as a potential ally in a more Saiyan - centered agenda.
One possibility is that Goku starts to remember more of his Saiyan past as Kakarot. Maybe he begins to have flashes of his original mission on Earth, which was to destroy it. This could create an internal conflict within him as he has grown to love Earth and its people. He might struggle with his identity, trying to reconcile the ruthless Saiyan warrior Kakarot was supposed to be with the kind - hearted Goku he has become.
I don't think there's a clear winner. Both Manga Goku and Manga Saitama have unique and powerful abilities. It could come down to strategy, luck, or even the author's imagination!