Leaving aside how this decision would be a completely contrived one for someone of Gohan's personality, even more so than his decisions in this arc already were, it's safe to say the Boo Arc occurs far differently. Piccolo joins the group in Babidi's spaceship, likely taking Vegeta's spot against Pui Pui. Depending on whether or not Goku would've seen Gohan still trains, either Gohan kills Dabura or Goku joins in to help him. Either way, no Boo. When BoG happens, there's one of two options:
1. SSG ritual doesn't happen but not having his day ruined by Boo, Beerus spares the Earth for its food. Months later, Freeza kills everyone and rules undisturbed until he either encounters Broly or Moro decides to escape from jail.
2. Goku uses the Dragon Balls to transport any surviving Saiyans to Earth. Tarble, Paragus and Broly appear, with the arc otherwise going the same. Having found Saiyan survivors, Paragus and Broly choose to stay on Earth for a while. When Freeza arrives, he murders Paragus, forcing Broly to go into a frenzy, kill everyone and destroy the Earth. He continues rampaging until Beerus is forced to fight him and barely wins, deciding to take Broly on as a Hakaishin candidate.
