Re Thain, yes.
Re Mizen, yes again. Knocking up was a role taken on from the old days oF the watch system, and was permitted only if it didn't interfere with regular duties.
I suspect that Mizen felt the woman was a drunk, which would have been a bind for him to deal with, so he dallied his response, hoping that a J division PC would pick her up. He venture out to Bucks Row was, possibly, a mere courtesy just to cover himself.