What if Batista successfully crushed the Castro brothers and their colleagues in Cuba? Would this prevent the Revolution from taking place?
The Cuban Revolution and ensuing Communist regime, yes.
A Cuban Revolution at some later point in time, probably not. My understanding of Batista is that he was pretty much an open crook, very deeply in league with the Mafia and American corporate interests, and completely lacking in legitimacy to govern. This man seized power in a coup, suspended the constitution, held obviously fake elections, and consistently responded to dissent with harsh repression rather than try to treat the root causes, like the stagnating economy & surging unemployment rates; no wonder people were lining up for years to take a crack at him even before Castro actually pulled it off.
Years before Castro's final victory,
another guy named Ramón Barquín already tried and failed to overthrow him - and Barquín was an elite Cuban Army officer with strong ties to the American defense establishment who was clearly deeply trusted by Batista himself, hardly a Communist firebrand. There were also
non-Communist rebel groups which fought against Batista and, in that specific case, got massacred trying to assassinate him at his palace. Clearly one didn't have to be a commie to hate Batista, just a Cuban patriot: and if Castro failed, just as Barquín and Echeverría failed before him, somebody else was inevitably going to try again and again until Batista's finally dead or overthrown.
Castro failing and somebody else succeeding in his stead would probably be the best for Cuba in the long run, anyway. Certainly Barquín and Echeverría didn't seem to be bad men. A victorious non-Communist rebellion that installs a regime which purges the corruption of the Batista years, without also going full retard re: socialism and getting embargo'd by the US, can only mean a more prosperous, less isolated and almost certainly actually more democratic Cuba that's better integrated into the American sphere & international politics generally today.