I can only speak about notoriety and recognition in the anglophone world.

Caesar, Antony, Brutus, and Cleopatra would definitely still be remembered without Shakespeare's plays. Having one of the most famous writers in history make your life into a narrative piece of theater is certainly helpful when it comes to staying in the public conscious, but these particular historic figures would probably have needed no such help. Especially Caesar himself.

These stories were already popular in England in the 1660s-70s when Shakespeare was young. Stories about the Roman Republic/Empire were considered essential parts of a good education. Latin was taught to students and portions of the works of Plutarch, Ovid, and Plautus were used as practice texts.

Plutarch's Lives was first translated into English by Sir Thomas North in 1597. It was apparently a great success, as orders for a second printing were recorded later that same year. This translation was almost certainly used by Shakespeare as the basis for his play as I discussed in a previous answer.

In addition to being yet another popularizing force behind the life of Julius Caesar & company, Shakespeare also became responsible for a number of misconceptions about the story: He compresses the events of several years into 5 days. He makes the Capitol the venue of Caesar's death rather than the Theatrum Pompeium. Shakespeare makes the Triumvirs meet in Rome instead of near Bononia. The period between Caesar's victory and Antony/Octavius regaining control is a span of 3 years, not one week. Caesar's assassination and the dueling speeches of Antony and Brutus happened months apart according to Plutarch while Shakespeare places all three events on one gigantically important day: The Ides of March. Shakespeare's final battle happens on the fifth day of the play, where Plutarch sets it months after the assassination.

To sum up, the public memories of Julius Caesar and Mark Antony were not in danger of fading when Shakespeare wrote his play. Indeed, he may have been responsible for as much confusion as awareness. On the other hand, Shakespeare made the character of Brutus much more interesting, conflicted, and three-dimensional than the one we read about in Plutarch. So I suppose it's safe to say that Shakespeare probably shaped the way we now view Brutus more than any other writer.