when I first started with a major airline here in the USA, boarding could even be done with the apu running and both pilots off the plane...f/a's had to be on board of course.
then it was changed to : one pilot had to be on board if the apu was running and pax were to be boarded or even remaining onboard on a through stop.
but if ground power/air was/were hooked up, the fa's would board without the pilots. Like the CAL guy above, sometimes non flying or "boarding duty" flight attendants would board for the crew while the flying crew was racing through the airport. Of course the pax would still have to wait while we preflighted and sometimes if we found something wrong with the plane, we had to have everyone get off the plane.
Now, I think it is better and safer to have the pilots and full cabin crew on board with the plane fully ready/preflighted in case something goes wrong...which it did one time.
The mx staff was changing a nosewheel, the plane was jacked up at the nose jacking point, pax on board. But the jetbridge (jetway) got caught under the main cabin door and the self leveling mechanism started to lift up the cabin door...until it and the plane slipped off and fell about 2 feet ...BANG.
I was on board as the f/o at the time (many years ago) and got on the PA system to reassure the passengers. It was this incident that made me want to do things the right and expensive way...full crew on board, to board.
The captain was walking between the jetway and the plane when it fell and he almost lost his head. The plane was damaged and taken out of service.
Be careful, don't be cheap...but that seems to be the order of the day.