@MikeT That question is a bit broad. Can you make FOG duplicate the SID, yes don’t sysprep the image before you capture it with FOG. Does FOG specifically duplicate the SID, no. Fog doesn’t care about the target OS. It just copies disk blocks from the source location to the target location. It doesn’t really step into windows.
So to answer your question a bit more directly. No the quality of your golden image determines if the SID is duplicated or not.