Considering his adaptation hax doesn't seem to allow him to surpass an opponent, he's only able to fight evenly with Boo and be at a disadvantage at first due to regeneration, infinite stamina and Boo's other abilities. When Galu arrives and the fusion wears off, Boo still absorbs Gohan, so how he fares against Vegetto comes down to if Boo can benefit from the progression hax too. If so, he proves a challenge for Vegetto, possibly forcing him to go SS2 or SS3, and Vegetto realises he can't toy with Boo; killing him instead and using both the Earth and Namekian Dragon Balls to restore everything to normal. If not, the events go just the same as in canon for the Boo Arc.
In either case, this discovery causes Gohan to not slack off and use his ability whilst still living his scholar life. For the dead Boo scenario, Beerus instead cordially asks about SSG after his pudding rather than going on a rampage and the scenario is unchanged for the regular Boo Arc route. FnF sees Gohan able to push Freeza a fair bit before Goku and Vegeta arrive, with Gohan helping out once Goku gets hit by Sorbet and helping avoid Freeza blowing up Earth. For the U6 tournament, he'd still be absent in the due to his conference. He'd be able to help out in the FT Arc even if not going to the future by helping Trunks, as well as possibly Goku and Vegeta, through sparring. If he's not busy though, he'd go in the time machine and offer some good support, though the overall outcome remains the same and just means Zamasu's hax gets brought into effect far earlier.
For the ToP, he'd already have progressed so much that he's able to defeat the fodder characters with ease as well as solidly defeat Kefla. Whether or not he can reach Jiren's level before being targeted and defeated is debatable, though he'd at least challenge Jiren enough to make U7's victory a lot smoother. Broly Arc goes unchanged seeing as how he was completely absent despite his power relevance anyway. Against Moro, he'd probably beat Saganbo or force him to overload on Moro's energy, but would ultimately lose to Moro regardless of how far he pushes him due to energy absorption and the arc remains the same, except in the scenario where Boo is dead in which case Galu and Vegeta may die on New Namek and at best would be unable to stop Planet Moro due to the absence of Oob.
