Krogan society never read to me as purely patriarchal. The smart warlord with the biggest krantt, clan, or quad gets to lead. If that warlord's quad happens to be ovaries, the lore allows for it.
In game dialog from ME2 indicted not only were females warlords, there were all-female clans. Females banding together for their own interests, sending out breeding requests to males they found worthy.
As for the godchild of quarians, I was amused. In that minor npc appearance, the devs showed the anti-cerberus element of humans that embraced another species as family. It is also not without precedent: in ME2, you played a character addressed as 'Shepard vas Normandy' by the quarians. It's just that kind of person who might join the Andromeda Initiative.
EDIT: if lore breaking elements of MEA trouble you, I found bright face paint on anyone not a Turian (or, apparently, Addison) annoying. Slapping it on Krogan and Salarians, when none existed before, detracted from the Turian lore.
