A complex endorsement is required to act as PIC of a complex airplane such as all Mooney M20's with the exception of the D model (if a fixed gear one still exists). Additionally a high performance endorsement is required to act as PIC of all post J Mooneys as they have over 200HP. So is there any way for a not yet HP/Complex endorsed Private Pilot to log PIC time in a Mooney? Yes! As long as they fly with another pilot or instructor who is qualified to act as PIC in a Mooney (including BFR, current, medical, and Complex/HP endorsements).
More about that and the story of how I got kicked out of a flight school for knowing more than the instructor here: