Yeah, I really don’t think King will be pulling from Hush. For one thing, the message is completely different in regards to the Bat/Cat relationship. In Hush, Batman ultimately proves that he will never be able to trust Catwoman completely because he’s too much of a paranoid detective. Catwoman then had no choice but to break off the relationship, acknowledging that maybe someday Batman will be able to get over himself and give Catwoman the trusting relationship she’s looking for.
With King’s story, especially now with the flashbacks, we find that Selina has known Batman’s secret identity for a while, and there is a lot more trust between the two of them. Also, I feel like since King is trying to make this story his own, I don’t see why he would want to spend time reflecting on other books that he didn’t even write. The first issue read pretty fast as is, so referencing Hush just wouldn’t be useful when he could probably do better himself.