With Freeza under his control and knowledge of a comparable fighter on Earth, Babidi would immediately set his sights on draining its inhabitants. With them and Dabura to assist him, the Cold family would have no issue in defeating Goku (and Trunks if this is the timeline he's travelling to) and the rest of the planet before moving onto their next target. They wouldn't destroy it, meaning whichever Artificial Human duo of the timeline still appears (though possibly a bit later due to more limited resources to construct them) but are ultimately given little to do with Earth's population already being heavily reduced. Shin would probably be drawn to Babidi's actions and be killed by Dabura. If Cell shows up, be it through time travel or decades passing, the heavily limited population for him to absorb would make him far weaker than in canon and he'd lose to Dabura even if becoming perfect, resulting in Babidi gaining another useful pawn (and possibly enough energy to fill Boo's tank if it's present Cell and Babidi's had two decades of journeying to other worlds). As long as Babidi never tried visiting Vampa, he'd rule the universe unchallenged with or without Boo, Moro remaining imprisoned due to Cranberry likely returning to the Freeza Force or being made a slave along with the Galactic Patrol at some point.
Tl;dr Babidi's absolute victory.
and 
2 I don't think they can revive buy.
