I can't see why not as we log SEP training P2 prior to license issue.
Because you cannot log P2 whatsoever in a Single Pilot aircraft. Single Pilot aircraft the only options are P1/PIC and PU/T. Plus a few exceptions for exam flights and integrated training. But P2 is reserved for Multi-Crew aircraft.
SEP training flights are logged as PU/T. So are TMG training flights. The only exception is if you are legally PIC (licensed, current and everything) but getting training nevertheless (clubcheck for instance). In that case you've got to decide (usually beforehand) who is going to be PIC. If it's you, the instructor logs nothing. If it's the instructor, he/she logs PIC and you log PU/T.