It's a great time to go...for about a million people. Seriously, we went this past Thanksgiving despite my warnings to my wife. She wanted to experience it for herself. We usually go every year at Christmas and the week end before Thanksgiving was about like a tipical summer day as far as crowds go, but as the week progressed toward Wednesday before Thanksgiving (our last day) they got heavier. In fact they were as heavy if not more so than Christmas Week and Easter Week (the two times of the year we normally go, my wife is a teacher and we are limited). Thanksgiving IS the third busiest week of the year, right behind Christmas and Spring Break. By the end of the trip, my wife said, "From now on we go at Christmas, at least then all of the Christmas lights are on at night!"
BTW, the Christmas lights aren't officially turned on until the week following Thanksgiving. They do start lighting them about Tuesday night before Thanksgiving, but its not official.