I wish I know more to answer you
but I think they can't reject it right away without requesting you for the doc. That's an interesting idea but I doubt if they can keep the original tracking number around for the later one to arrive, it seems tricky .. how would they know about the second envelope when opening the first one.. May be once they enter the application into the system its possible to send the doc to attach to the application before they ask as you'll have a file number. But I must say, I don't know if this is possible. Is there someone else on the forum who can answer and knows better ?
