Yes, the calendar does update in real time. When you see an opening, do not hesitate to take it. When you see availability on a sold-out day, it’s because someone canceled a reservation. Which means there might only be 1 spot available and, by the time you click reserve, it might already be gone (this is what happened to the poster above). Likely, cancelling your reservation and then trying to book it will take too long. You will have to cancel your reservations now, and then be ready to book at a moments notice. My daughter’s friend invited her to go to DL a week before their family was going. The Saturday they were going was sold out. I spent about an hour diligently refreshing the reservation calendar. The day became available several times, but it wasn’t until the 5th time that I was fast enough to snag a reservation.
Disney does occasionally release large blocks of reservations. I believe some DISers have figured out about when this happens. Maybe someone else will chime in that’s in the know.