Note that even if they are "looking for" only customers without connections you might be able to talk them in to taking you as a VDB even if you have a connection just tell them you are flexible, etc. I would not worry about your luggage too much it will go on to your destination andyou can pick it up at the UA bag service office whenever you get there. If you check the bag at the ticket counter and tell them you want to volunteer they may tag the bag standby so that perhaps it will be held back. Also very occasionally they take VDB's at the ticket counter and process the whole thing at the counter if they absolutely know they will oversell. But this has only happened to me once, e.g. I was taken off as a VDB even before boarding started. But LAX is a great VDB city I've been bumped out of LAX a number of times.