I would expect it to be nuts the whole holiday week (kids usually start getting their days off from school earlier in the week, and off people go on their trips)
On the flipside, though, I have gone on both Disney and Universal trips several times the week after Thanksgiving (usually starting the Sunday after) and its generally been a wonderful time to visit. Lighter crowds the entire wee (for Disney and Universal, never expect "dead" at these places, but FAR from anything resembling peak).
Yes, I imagine most who planned to stay over FOR the holiday, all probably ship out either Saturday or Sunday- back in time for kids to go back to school and such.