Extremely close, but not quite, Jinpachi formed the Zaibatsu, over time he taught his son the ways of the business and martial arts, but Heihachi eventually became hungry for power and overthrew his father, beating him savagely, he had those who opposed him killed and had Jinpachi locked away under Honmaru, where he died a slow death from his beatings and starvation among other things.
So you were close, incidentally, I still have not figured out why Heihachi lacks the devil gene, the Mishima clan seem to have it and are able to 'activate' it when in contact with the beast, but Heihachi seems to have skipped a generation, seems he's the black sheep, no pub intended to those who understand genetics.