That's another gray area, thanks to the FAA. My understanding is that pilots cannot log PIC in a complex until after they receive the complex endorsement.
61.51(e) A recreational, private, or commercial pilot may log PIC time only for that time during which that person is the sole manipulator of the controls of an aircraft for which the pilot is rated.
The FAA defines rating as: A statement that, as part of a certificate, sets forth special conditions, privileges, or limitations. The complex endorsement could be considered a statement of privilege, and therefore is necessary to be rated in and log PIC time in a complex aircraft.
That's my interpretation. Call your local FSDO and ask what their interpretation is.