Probably not. First, Vito would never carry a gun because, as a well-known Mafia Don, he'd be a constant target for law enforcement. If they ever saw him with a gun, or even spotted a bulge under his coat, they'd arrest him on the spot for carrying. He could have been sent to prison for years on that charge alone. Second, Vito didn't need a gun because he had bodyguards. Admittedly, his regular bodyguard (Paulie) sold him out, and his substitute (Fredo) fell down on the job. But even so, he was the victim of an ambush by professional assassins that he hadn't anticipated. And even if he carried a gun, he probably wouldn't have been able to get it out of his coat in time.