We can't be certain of anything that deals with the hypothetical. While the death of Antonius might seemingly allow a peaceable return to Republican government, we can't be certain that another ambitious general wouldn't have seized an opportunity to fill the power void. Perhaps a Lepidus, Decimus Brutus, Aulus Hirtius, Sex. Pompeius, etc. would've made a tangible bid for power. Some may be more likely candidates, others perhaps would've surprised us, but different circumstances can create different behavior. Consider too that without Antonius, perhaps a great many more of Caesar's veterans would've joined the young Octavius. I don't see any reason to believe that he wouldn't have come to Rome and asserted his rights as heir. The absence of Antonius creates an interesting dynamic in this regard, but I certainly don't think it changes the young man's ambition.
Of course, with that said, the death of Antonius would've made a return to Republicanism much more likely, but there are always potential variables.