Actually it's the load controllers who control the computer close off, and so they are the only ones who can 'reopen' the flight and except you as 'LMC's' (Last Minute Changes). It all depends on were your aircraft is(for remote & bused stands, forget it!) & how busy the airport is (how quickly you'll get through security), as to wether they'll except you. The loadie may or may not consult the captain of the flight concernd depending on how close it is to the slot time. At the end of the day the captain WILL generally support the ground crew decision in this matter. So my advice is leave PLENTY (and I mean PLENTY) of time for getting to the airport, so that you can complete check-in before it closes for the flight.