The log book would be signed or stamped by the CFI to show a completed training course, not an individual flight.
However, there is nothing to stop one of the flights being used as the "training flight." I certainly would have no issue with that, it's just that the logbook would need to be annotated to meet the requirements.
Not something that would be done as a matter of course unless asked for, though I certainly ask people when their SEP rating runs out so if we can meet the requirements as I see them in a "normal" training flight, then that would be sensible rather than wasting a members money and time doing an unnecessary and seperate flight when with just a signature you can fulfil the requirements as long as the student has flown to a decent standard, which would usually be a formality if you've done something like a night rating course with them.