Difficult to say. At that point, it seems unlikely that Caesar would have ever restored the Republic. He held the senate in a state of some contempt. More than likely, if he hadn't been assassinated, he would have died of old age, at which point his will would have been read, and Octavian would have been his heir. I think if that had happened, the transition of power would likely have been smoother, since Caesar would have had more time to acclimate the Roman people to 1-man rule and so the series of civil wars would likely have been shorter, if not nonexistant.
Also, just a word of advice - I would basically ignore everything Shakespeare has to say on Roman history. He's not a historian and is more looking to entertain an audience/give them something to think about. Many of his details are wrong. If you want a good account of what happened, I would suggest either reading Suetonius or Plutarch's Life of Caesar or, better yet, take out a biography - I recommend either Meier or Goldsworthy. -M
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