Luca was Vito's man to the death--Vito's or his. Sol knew that, which is why he waited until he killed Luca before trying to kill Vito. If Luca had survived, he'd have moved heaven and earth to avenge Vito. As Hagen told Sol: "Not even Sonny will be able to call off Luca."

If Vito had died of natural causes, it's a question if he'd have transferred his loyalty to Sonny or Michael. Luca was his own man, he had his own reasons (as the novel points out) to be loyal to Vito, and as we saw in the film, Vito saw him alone, without Hagen as intermediary. On the other hand, the Corleones were his only family, and provided him with a rich living.