but I was always under the impression that you were not 'Qualified' to operate in a seat until F L Check.
Fare paying passengers can not be carried on training flights.
On a training flight the instructor has to hold an appropriate rating i.e. TRI / TRE.
Line training using Training Captains who are not TRIs or TREs with fare paying passengers onboard can only be done if the pilot being "trained" is legally qualified to fly the aircraft in that situation.
A multi crew aircraft must have two qualified pilots. If we follow your line then we can never do line training with passengers on board.
Finally, in your airline, what is the procedure for a training Captain who needs a physiological break while line training an experienced (but not line cheked) FO?