Depends on how you think the others would have reacted. It seems that
the only reason they decided to confront RRA was to save Goku; without
that motive, they'd have been too scared to attack. Also, Roshi stated
he was not sure he had the stamina to win against all of them (obviously
referring to his buffed form's drawbakcs, considering he'd need his buffed
form to take Black or Taopaipai). So, there are three cases...
1. Goku's crew is too scared to attack
RRA takes over the world. When Red uses the wish to get tall, Black gets
angry at him and kills him, so RRA continues under Black's leadership.
Taopaipai continues his career as an assassin. Tenshinhan eventually
gains the power required to free the world, but it's not known whether he
ignores RRA and becomes an assassin or whether he somehow sees the
light, realizing he's not cut out to killing. In the second case, he frees
the world and becomes a hero.
I think Pilaf's gang releases Piccolo anyway, because they wanted to take
over the world regardless of Goku's existence. Considering the flow of
events is different this time, maybe either Roshi or Tenshinhan manage
to seal him (either Roshi doesn't miss or Tenshinhan's jar doesn't break).
When Raditz arrives, he eliminates all life on the planet.
2. Goku's crew attack, but they lose
Same case as above, except Piccolo's plans are more likely to succeed,
considering Roshi won't be there to try to stop him.
3. Goku's crew attack and win
They use the dragonballs to revive Goku. 1 year later, Goku gathers the
dragonballs again to revive Upa's father. At that point, maybe he learns
about Korin's tower, so he does the same training and 22nd TB events
procceed as we know. If he doesn't train with Korin, at 22nd TB, he's a
lot weaker than in canon and gets defeated by Ten in the final. At that
point, Ten will either realize he doesn't want to be an assassin or procceed
to kill Goku.
If he kills Goku, Piccolo takes over the world until Raditz eliminates all life
on the planet. If he doesn't kill Goku, tough to say. There are still many
points Goku might die: Against Yadjirobe (assuming it wasn't just a gag
fight and Yadjirobe was going for the kill), against Tambourine, against
Old Piccolo.
If Goku somehow survives all that, it depends on how Holy Water works.
If you view it as a multiplier, Goku ends up weaker than Young Piccolo and
loses. If it's a potential unlock, then, after drinking it, Goku ends up as
strong as in canon, so the events after that proceed as in the series.