I think he did know. In fact, he might have told her never to unsheathe her sword unless he is not there to protect her or something,
I have a feeling her power is going to be crazy and I do believe she has a bankai,
It's obvious Kenpachi knows, that's why she said she could used her sword because Ken-chan wasn't around.He probably doesn't want her fighting.And the fact that she has been the lieutenant for so long an never been unseated in a squad that had two shinigami who became lieutenant of other squads, Renji and Tetsuzaemon, and two shinigamis who have bankai Renji and Ikkaku shows Kenpachi must have knew of her strength.
zaraki knows about her power but there is no need for her to fight everytime because he was there to save her and this is the 1st time we have seen her fighting without zaraki.