User blog comment:B214/Talk About What You Want! 3/@comment-24098614-20150329012653/@comment-1359322-20150329013140

Yes, Ise and Rias' child won't be considered as Pure-bloods. And yes, none of them are eligible for the position, but it's not because of just Devil laws or thinking, because there's also the fact that Rias only took over as Clan Head because Sirzechs became Lucifer, so the rightful Clan Head position belongs to Sirzechs' descendant not Rias' descendant.