One good turn deserves another, Don Cardi. Let's take your interesting and novel question one step further:
Suppose Jules really was Vincent's father--he impregnated Lucy after performing the famous operation. But then he disappears--runs off with another woman, hit by a truck, goes to jail for performing all those then-illegal abortions, whatever. Now Lucy's the unwed mother of an illegitimate child, a bad place for a woman to be in that era.
But she gets a brainwave: Why not claim that Sonny was Vincent's father! That way, the Corleones will have an obligation to him, and to her. Of course, Hagen or anyone could see through that story simply by comparing the dates on Sonny's death certificate and Vincent's birth certificate. But clever Lucy enlists Connie in her scheme! She and Connie were bosom buddies (she was Connie's maid of honor). Connie likes the idea because she can use Vincent as a proxy to assert herself in the Family, after the Carlo fiasco. So Connie adds her influence to the Vincent-is-Sonny's-son story, and it carries. Then we get GFIII...