The Amber series has there "Cowl" figure end up being a female behind a mask. Same female ends up being involved in a "I love you" plot. She also was an ex-girlfriend of the protagonist.
This is a discussion about The Dresden Files. Not for the Chronicles of Amber. It's a fine series, but it really has nothing to do with the plot of Dresden.
I am firmly in the "no" camp on this theory. There's nothing in any of Faith's interactions with Harry that suggest any kind of connection at all, there's nothing in her behavior that suggests she has had any experience with the Nevernever, let alone having lived there for a chunk of her life, and shoehorning her into Harry's backstory does nothing to benefit the series as a whole and requires jumping through far too many hoops for it to make any amount of sense.
I don't see any point to it, and frankly it cheapens the series to have everything come from such a small world that everybody in it has to be intrinsically connected. It's like having Anakin build C-3PO.
Characters can appear in the series without having been previously connected to everyone else.