I've gone four or five times during the week after Thanksgiving (and will be doing so this year as well, arriving on the Saturday after Thanksgiving and staying 7 nights).
Obviously, I keep coming back from more! Generally, you'll find that the crowds are fairly heavy, maybe even extremely so, the weekend after Thanksgiving. But by late-afternoon Sunday, most of the Thanksgiving week vacationers are jetting back to their lives, leaving the rest of the week for you to enjoy the parks with minimum crowds. This holds true for Universal/IOA as well (I generally go over and am able to hit all the major attractions at BOTH parks in one day!).
I don't know if discounts and the like will impact things this year, but based on past experience, I'm thinking you'll have a great time! (I should say "we'll have a great time" since I'll be there too!)
Richard