If you mean that bonuses of superior commanders will apply, if there is still non-destroyed HQ in the chain - no, IIRC they will not. Bonuses of superior commanders applied only if there is uninterrupted chain of commanders (with proper ranks), not HQs only.
Yes, as I wrote above, if you have no RP rule to not teleportate commanders from some other place inside ongoing combat to replace killed officer - well, yes, then you have an option to replace killed commander effectively. But it's exploit, because IRL in this case replacement commander must be inferior-rank commander from the same formation, not a new-assigned commander of the same rank as just killed one was. And in Aurora you cannot assign inferior-rank commander in the place of their killed superior commander and rely on their bonuses and bonus-transmission, because this new commander must have proper rank, not a lower one, to apply their bonuses and bonus-transmission. There is no temporary promotion mechanism in this version of Aurora (IIRC, it was sugested, but I don't know if Steve have a plan to implement it), so no "step in", if you cannot manually find, promote and reassign one of subordinates, that have proper Ground Combat Command rating (I think it will be rare case: such commanders normally have their promotions at non-combat time, not awaiting their superior KIA to replace them). So, exploit or suffer.