No, at the time that Buffy said that she knew that Dawn wasn't actually part of her family but what (not "who," which I find significant in this content) she was, was was pretty much a total mystery to everyone at that point, a set of memories that they were just beginning to realize were totally false. Almost certainly, Buffy was thinking about her original college roommate, a demon trying to, for some undisclosed reason, was trying to pass herself as human. And on that note, I've always wondered if the mysterious monks, if any of them had survived their confrontation with Glory, had any plans of actually telling Buffy just what Dawn really was and why she had been placed in her care. She found out eventually anyhow, and it certainly didn't lessen her determination to prevent Glory's plans from being successful.