I don't think so, his ethnicity was Punic. His ancestors came from Lebanon.
The important thing to note about Punic society is that ethnic Carthaginians rarely went into the military. It was a mercantile society, if you were Punic generally you went into business and politics, not soldiering. So armies were largely built up by hiring mercenaries of diverse backgrounds. Drafting was restricted to non-Punic lower classes. Command usually remained for Punics.
Hannibal's most important unit was likely made up of black men, the Numidian cavalry. Also the skirmishers - archers, slingers, and javelins - would also have been recruited exclusively from the Numidian population. There were also some mixed race Libyo-Punic spearmen he relied a lot on. Otherwise the rest of his army consisted of cacs - the Gallic and Iberian mercenary infantry.
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