Yes, the likelihood is very low. BGW has 40+ years of historical attendance records to draw up algorithms. So they open up for 10k reservations. They'll have a pretty good idea of the percentage of no-shows and they might actually be able to handle 12-13k so if that NoVa family shows they'll quietly let them through.
@WDWRLD I suggested (surmised) that the reservation system would allow just that...allow for reservations for a few days. They'd have to do that to accommodate the tourists coming down to Kingsmill Resort for a week of history, etc. I would think they'd only allow a maximum number of reservations per login, though so some jerk doesn't yet to make a reservation for every single day.