I have been there twice the week after Thanksgiving, 2009 and 2011. And i LOVED it. The crowds are lower but still busy. But it's more people walking around crowded than Rides Busy crowded. The only rides that were long waits were Soarin and TSM and back then they weren't expanded gates/tracks. Plus, I used FP for both so no biggie. No problems with dinner reservations. The ONLY time the crowds got to be too much for me was HS during EMH at night but, of course, what drew in those crowds were the Osbourne Lights, which are sadly gone now.
I've been there many different times of the year and the week after Thanksgiving is by far my favorite. The decorations, the lower crowds, the music, the holiday cheer....just incredible. ENJOY!!!!!!!!!!!