In my company, the captain is "...responsible for the safety of all crew members, passengers and cargo on board, as soon as he arrives on board, until he leaves the aircraft at the end of the flight."
This would suggest that if a passenger should become injured whilst boarding, or prior to the arrival of the captain, then there would be no-one officially responsible for that injury. It would hardly be fair for the captain to be made responsible for this injury and have to complete accident forms and ASR's etc. Would that be the responsibility of the No.1?
No, I cannot see any reason to board without flight deck crew. It makes no sense. If the ground staff want to expedite boarding, get the passengers ready at the gate or get the bus waiting outside the aircraft ready to board as soon as the crew arrive. After all, even if they are all sitting in the cabin, the cockpit crew still have to do their checks which could be done whilst they are boarding.
If there was a MEL item that precluded boarding, would the cabin crew know that or be aware? I suspect not. This is a case where the 'tail is wagging the dog.' Captains at these airlines should put their foot down and not accept this ridiculous policy, clearly imposed by management types and beancounters who have no clue about aircraft operation, other than delay codes. Time to put the capital C back into Captain!