It's an interesting question. Every FTO I trained at and taught at in the U.K. allowed post-solo students to start up without the instructor being on board; never considered it to be an issue. Never been to a school in the U.S. however where it has ever been permitted. Bit like F/O's not being allowed to taxy in most U.S. airlines.
B2N2
No time to quiz them and ask systems questions during the start-up procedure.
Why would you want to distract them during start-up? I've seen this many times in the U.S. - almost constant interuption from the FI during a procedure with questions like "what's the purpose of this or that" or "why do you start with one magneto rather than both" etc. Let them get on with it and if they make a mistake either intervene appropriately or let them realise on their own and correct it, make a note then....discuss in the debrief.