Yes, yes she is. During the last event literally everyone of her lines is about Enterprise. Even her secretary quest, which is supposed to be about the player bonding with the shipgirl, is more about Enterprise than anybody else. Zuikaku isn't even as bad as Essex, she actually talks about things besides the Grey Ghost from time to time.
Welp, their parents took this situation really well... Now that I think of that, maybe my parents would be delighted to have a clone that is the opposite of me.