No, because it has to be a soul, Rei from what I understand does not have a soul and if she does it's probably a fragment of Yui's or something. I have seen theories that say it's Ritsuko's mother inside that thing. The dummy plug system barely seemed to work and Unit 0 went berserk far too often for it to be a competent test bed for the system.
Ritsuko's mom is the magi computer, can't be her.