No, and I should really add neither.
P1/S or PICUS is for a U.K. CAA flight test only. Many CAs outside the UK frown upon this at PPL level. Whilst it is an acceptable practice as far as the uK are concerned I should point out that CAP804 is a U.K. document for reference only and is not currently updated nor EASA law.
Furhermore, when you do your recency check who signs the tech-log? If it is your CFI then it should be them that logs P1 and you U/T. There is no such thing as P2 or Co-Pilot for single pilot operations- and the only time there are considered two crew in those circumstances is when it’s an instructional flight and the other guy is the examiner/instructor.
However, it’s your logbook.....the only time it may be an issue is if claiming P1 time for CPL.