This is a matter of pure speculation, because Brutus did join the conspiracy and history records what happened. It seems that there would have been two possible outcomes if Brutus had not joined the conspiracy. First, Cassius might not have been able to recruit other men and there would have been no assassination attempt. Then Caesar would have gone on to become king and perhaps emperor and finally a god. On the other hand, there might have been a conspiracy and Caesar would have been assassinated, but the Roman people might have turned against the conspirators, as they did anyway. Marc Antony would have found it easy to form a triumvirate with Octavius and Lepidus, or perhaps just a partnership with Octavius, which was what ultimately developed, as dramatized in Shakespeare's Antony and Cleopatra. Cassius and his co-conspirators would have had to fight the forces of Octavius and Antony and could have been defeated much more quickly and easily without Brutus and the many soldiers he could recruit because of his famous name.
Cassius is aware that he desperately needs Brutus to lend legitimacy to the assassination and to help form a new government after Caesar is disposed of. Cassius is not well liked because of his greedy nature and his bad temper. He would like Brutus to be a figurehead while he himself would be the real leader in the new government he hopes to form. Brutus would never have joined this conspiracy except for the persistent efforts of Cassius to draw him in. At the end of Act 1, Scene 2, Cassius shows his cunning nature in a soliloquy and tells how he plans to exert further pressure on Brutus by appealing to his patriotism.
I will this night,
In several hands, in at his windows throw,
As if they came from several citizens,
Writings, all tending to the great opinion
That Rome holds of his name, wherein obscurely
Caesar's ambition shall be glanced at.
And after this let Caesar seat him sure;
For we will shake him, or worse days endure.
It seems most likely that if Brutus had not been persuaded to join the conspiracy, the assassination would not have been attempted. The conspirators needed a strong leader, and Cassius was a mediocrity. When he and Brutus are arguing in Brutus' tent in Act 4, Scene 2, Brutus says, "Away, slight man."
We see in Act 1, Scene 2 what a hard time Cassius is having even getting Casca to come to his home. Casca is quite rude to him.
Will you dine with me tomorrow?
Ay, if I be alive, and your mind hold, and your dinner worth the eating.
We only see Cassius trying to recruit two men, Brutus and Casca. But it is generally known that Caesar dislikes Cassius, and the people he approaches, such as Casca, are reluctant to be seen with him because they are afraid of Caesar. Cassius is motivated by fear. He senses that Caesar might have him killed if Caesar obtained absolute power. Cassius might find it impossible to organize any conspiracy by himself. Everybody is afraid of Julius Caesar. It takes something like thirty men to assassinate him, and these men might never have joined in the plot if Cassius had been the leader. Most of them might even refuse to talk to him, knowing that he is just as ambitious as Caesar but lacking Caesar's charisma, achievements, popularity, and military backing. Cassius himself might not have thought of attempting to assassinate Caesar if he had not been afraid of what might happen to him if Caesar gained absolute power. In his soliloquy at the end of Act 1, Scene 2, he says:
Caesar doth bear me hard, but he loves Brutus.
If I were Brutus now and he were Cassius,
He should not humor me.