We have gone during Thanksgiving week several times, and it's one of our favorite times to go. It's not too busy Sat. through Wed. prior. On Wed. is when large numbers of people start to arrive (more schools are out Wed. - Fri. than the entire week, I guess). The rest of the week is very busy, but if you plan your touring carefully it doesn't need to interfere.
DO NOT PLAN TO GO TO THE MK ON THANKSGIVING DAY! The MK receives loads of local and out of town visitors and very often is CLOSED by 11 am. We usually go to Epcot, and often have walked right onto things (haven't been there at Thanksgiving since Test Track opened, so can't vouch for that attraction).
Definitely make PS for Thanksgiving Dinner as far in advance as you can!
The Osborne Family Lights at MGM usually open Wed. night, so be sure to see them sometime that week too. They are spectacular and get more beautiful and amazing every year.