I don't remember Rome very well, but depending on when this incident is supposed to take place, no they wouldn't. Among the more horrible deprivations (for Italy at least) of the wars of the triumvirs was the near-total stranglehold Sextus Pompey had on the grain supply from Africa. Following his proscription in 43 Sextus Pompey assumed total control over Sicily and Sardinia, cutting off the grain supply from those two vital provinces--by 40 he had invaded Corsica and was making landings in Bruttium at the south of Italy in support of Lucius Antony's Perusine War. Sextus Pompey cut off the grain supply from Africa and Sicily so effectively that despite the Pact of Brundisium the triumvirs were forced in 39 to recognize Sextus Pompey in their schemes as governor of Corsica, Sicily, Sardinia, and Achaea in Greece with the Treaty of Misenum. He was never able to fully extend his control over Africa and lost Corsica and Sardinia in 38, but his last years of control in Sicily were some of the most horrible for the city, as Sextus Pompey's fleet actively pursued a policy of blockade and was fairly successful for a time at preventing Agrippa from decisively defeating him. I can't think of any time at which Antony cut off the grain trade from Egypt (which would not necessarily have been particularly successful), although there might be something I'm forgetting--what you're describing seems to suggest more an attempt to make reference to the disruption of the grain trade by Sextus Pompey, who as I recall is not actually in the series at all