In case the Gambit conditions are met all power goes to the male heir, until he is ready to rule his parents will have full control. So no, as soon that happens any chair on the board is effectively powerless.
The gambit is the will of Alexander Karlson, it's his way to enable his wish for a male heir from his and Callista's bloodlines, even after his death. We don't know the exact rules the sisters and Kane have to follow, but it's clear the Gambit Queen is one of the people responsible for a fair process, but even the boardmembers will help ensuring this, after all it's their chance to become more powerful or lose power. Four of the board members have a fair chance for more power....
Knowing Alexander he couldn't care less if Kane ends up as a slave, but knowing Calista prepared her children for this (even if only one of her blood) , it's safe to assume everybody will have a fair chance.
It will not matter if Kane is sub or dom, the rules for the Gambit will be the same, Kane might win the Gambit being a sub to any of the Karlson sisters or Olivia, he might win the Gambit as a dom or equal to any of them as well...