Well for one, it'd make it so there was some actual stakes rather than being an extremely long piece of filler.
I'd say the general scaling prior to the God ritual would be the same. SS3 Goku and SS2 Vegeta surpassing Ultimate Gohan prior to the ritual and rage boost respectively are already going way beyond what their limits ought to be and I doubt Oob would be able to access his full potential just yet, at best being SS3 Goku's equal. After the God ritual, Goku would continue to spar with Oob when not being taught by Whis and with what we know of Boo's potential from the manga's current arc, Oob would definitely be one of the top tiers of the main cast. I don't think he'd be able to make such strides instantly though, so he'd be more or less on par with Goku/Vegeta in most arcs and prior to the ToP his only plot-changing role would be making the U6 tournament an easier win for U7, especially if we're talking for the manga continuity where if placing him at around SSB tier, he may be able to beat Hit if not succumbing to his skill. He would have little role in the Future Trunks Arc due to limited space in the Time Machine.
For the ToP, I disagree that he would replace Tenshinhan and would instead replace Boo/Freeza's spot. Going by the manga continuity (because Super's anime powerscaling is the most inconsistent thing in the franchise), I'd say he ought to be equal to Boo's current self, which I'd place more or less on the level of Peak ToP Gohan/SSJ Kefla. With far more raw power than Freeza and significant skill from being trained by Goku for years, he would be the powerhouse of U7 prior to SSBE Vegeta and UI Goku and would allow for the victory against Jiren to come a fair bit easier, provided he wasn't taken out by a sneak attack such as Damon's off-guard attacks. He may have a role in the Broly or Moro Arcs if not going back to his village, though not by enough to aid in any meaningful way. If anything, him being there as an energy source for Moro would benefit Moro, though likely not change things by much when considering how Dai Kaioshin suggested Moro's taving of his prime power was just an excuse and he seems to have some backup plan to make him just as deadly anyway.
He'd also meet up regularly with Old Meng Chappa and by being introduced to the main cast such as Roshi, Chappa would learn the secret of Manly GAINZ.
