Absolutely essential. By all accounts Octavian was never more than a middling field commander. While Octavian had the killer instinct and shrewd grasp of political affairs that helped him to get his foot in the door of Roman power politics after his uncle's assassination in 44 BCE, it was the campaigns Agrippa won for Octavian (putting down rebellions in Gaul in 38 BCE, against Sextus Pompey in Sicily in 36 BCE--crucially after Octavian's failure to defeat Pompey on his own had seriously shaken his political legitimacy in Italy)--along with Marcus Antonius' own failings in his eastern campaigns against the Parthians--that kept the Roman Senate from throwing him over and siding wholesale with Antony when the political rivalry between the two men finally hit full boil. Agrippa's military successes MADE the younger, coldly standoffish, oft-embattled and occasionally cruel Octavian seem a viable prospect against the more seasoned, publically loved, and militarily tried-and-tested Antony. And, of course, without Agrippa it is unlikely that Octavian would have managed to achieve the smashing victory at Actium in 31 BCE that left him the sole master of the Empire. Even given Antony's tactical blunders in the battle, anything less than overwhelming defeat would likely have given Antony's forces cause to hope (as had been the case in Northern Italy a decade before), and they would almost certainly have regrouped for continued fighting. Octavian's forces, by comparison (without Agrippa) would almost surely have folded after a single defeat.

After the defeat of Antony, Agrippa's contribution to Octavian's regime became slightly LESS central, but only slightly. Agrippa's competency as not just a general but also as a civic administrator and urban planner would be crucial to Augustus' plans to turn Rome from a city of brick into a city of marble, and helped to endear the new Imperial regime to the people of Rome, who benefited from many of the public buildings and civic improvements that Agrippa introduced. And although Agrippa ceased to be instrumental in winning major military victories that solidified Augustus' legitimacy, the new Emperor's increasingly poor health and inability to find a blood heir who could live long enough to inherit his powers meant that Augustus had to turn to his friend on several occasions in order to hold power on behalf of the regime while he himself was so ill that it wasn't even certain whether he would survive. It was only Agrippa's known competency as a general and administrator that allowed him to hold this position without leading to renewed factionalism and civic strife within the Empire. Had a younger, less-seasoned man (Tiberius or Drusus, for example) been entrusted with the position, it is likely that some Senatorial magnate (or a united effort from those elites who still had it in them to resist) would have challenged the regime and potentially driven the Caesarians from power before Augustus could recover.

Agrippa was utterly crucial to Octavian both rising to power and holding onto power long enough for the new Imperial regime to solidify its hold on Rome. In his early and middle years in power, Octavian/Augustus lacked several crucial qualities which his uncle had used to great success in securing his own position at the top of Rome's social order: his lack of military brilliance and success and his ability to win over the people through crucially needed civic reforms and public building. Agrippa provided those qualities in spades. Augustus also lacked much of his uncle's sense for how to win over the middle and upper-classes at Rome and throughout the Empire (in part because for in early years of his dominance he murdered a whole bunch of them), a deficiency for which he would turn to his other close friend for much of his rise to power: Maecenas. In effect, it took all three men--Augustus with his brilliance for finding and seizing political advantage and outmaneuvering political opponents, Agrippa with his battlefield successes and flair for winning over the people through civic reform and public building campaigns, and Maecenas with his ability to woo the artistic and social elites of Rome and win them over to the Augustan regime--to match (and perhaps even slightly exceed) the overwhelming political and military genius that had been Julius Caesar.

Remove Agrippa from the equation and the whole house of cards comes crashing down.