I guess the same thing that happened to Xander's soul while he was possessed by a hyena, and to Spike's soul while he was possessed by the First Evil. Possession is a very common theme is both BtVS and AtS, it seems, but the writers tend to stay none-specific about the memories business. It would feel seriously disturbing if Cordelia herself was present and silently screaming/or enjoying herself ? during all her scenes with Connor. Then again, its Whedon's show. At least the Dolls never remembered their assignations...