I don't think so.
Remember that in reality, Caesar established Pompey as his legal heir from 59 BCE (the marriage with Julia) to the civil war. He made his will public during the civil war in order to prove he had always wanted to remain in good terms with Pompey.
Of course, as any roman noble, Caesar wanted to make sure his lineage would last beyond him. And for this he took the usual "insurance" to which sonless romans resorted : adoption.
However, there were risks against which no insurance could legally, nor even humanly, be subscribed. You could never be sure that a son, be he your biological son or your adoptive son, would live.
There are several examples of famous noble families which extincted although they had sons or had resorted to adoption.
It was the case Lucius Licinius Crassus (not the line of the triumvir), consul in 95 and censor in 95, who had only 2 daughters (one married to Marius the younger, the other married to Publius Cornelius Scipio Nasica). Crassus adopted one of his grandsons by Scipio Nasica (this grandson being the brother of the Quintus Caecilius Metellus Pius Scipio Nasica who would be consul in 52). But this grandson/adoptive son died young, after the death of his grandfather/adoptive son, so the lineage got extinct.
There si also the famous example of Lucius Aemilius Paullus Macedonicus who had 4 sons. He gave 2 by adoption, but his 2 remaining younger sons died before their father, and they died childless.
And Sulla himself, very similar to Caesar in many points except that he was merciless instead of clement, face the situation of dying with only a 7 years-old son left. At that time, there was a great risk that children would not reach adulthood, even in the nobility. Sulla did not try to take adopt another son to prevent extinction : that was an unavoidable risk seen as fatum which everybody was prepared to face.
Well, Octavius had a poor health and nobody would ever had bet that he would live so long.
And if Caesar, in his will, named no other adoptive son in the case his son would die (he just named second rank heirs), I think it's because it was not legally (and understandably) possible to have delayed adoption in your will.
And besides, although the octavian/augustan propaganda strove to make people that Octavian was predestined from even before the craddle, he was not. He was not part of the scheme as long as Pompey and Caesar remained allied. He would have been even less in the WI we're discussing about, with a grandson born from the union of Pompey and Julia.
And even in real history, Octavian was secretly and temporarily adopted only in 45 BCE. Between 48 and 45, there had been an other heir : several scholars astutely guessed it was Caesar's cousin Sextus Julius Caesar (murdered in Syria late in 46 BCE).
So I really see no room as adoptive son for Octavius in this WI. But I can understand that for us, with our difficulties to measure to its full extent the possibilities of alternate histories, it's hard to accept that Augustus' life was all but likely.
