Whichever way you log it, it will count towards your total time. But it cannot count towards your total P1C time because you would NOT be the Commander - the FI would be.
We've gone autonomous on this at my RF and have standardised as follows:
Training Flight for SEP Class Rating Re-validation. As most will know, one option for the re-validation of SEP Class Ratings is ‘By Experience’. This includes a 1 hour ‘Training Flight’ with an Instructor, although this may be replaced by any Skill Test, Proficiency Check, flight with a military QFI in the course of military duties or IMC flight test. There has been much discussion as to who may log what for this flight; so to standardise, we’ll be adopting the following policy:
a. SEP Re-validation LPC, renewal LST or IMC Rating flight test: FE is P1C, pilot is P1S. If unsuccessful, pilot is Pu/t.
b. Annual Club check or 1 hr SEP training flight: FI is P1C, pilot under supervision is P1S as he/she's merely carrying out a series of mutually agreed events within the privileges of his/her licence with the benefit of friendly advice from the FI. The pilot is not 'under training' for anything specific, neither is he/she under test. FI signs pilot's logbook to confirm that this was a satisfactory flight for the purpose of SEP revalidation by experience. Exceptionally, if the FI is not happy with way the flight went (which I hope will rarely be the case!), he/she should not sign the logbook as that's the CAA Chief Flight Examiner's current guidance. Recommended training should be discussed and proposed (and copied to the CFI); the pilot will not be allowed to fly as Commander on a Club aircraft until such 'recommended training' has been satisfactorily completed. The flights for recommended training will be flown with the FI as P1C and the pilot under training as Pu/t.
In a nutshell, the FE or FI is always Commander, the other pilot is either acting under supervision (PIS) or under training (Pu/t). The idea of the SEP training flight is to help you stay safe, not to put you under duress. Treat it as a chance to brush up your skills and enjoy it!"
Perhaps that's too obvious and logical for the JAA? But we haven't had anyone performing unsatisfactorily during their 1 hour training flight either!