We've been to HH for Thanksgiving four times; this year will be our fifth.
The resort does have turkey dinners -- either roast or deep-fried -- with all the trimmings. As I understand it, they are quite generous with the portion sizes!
I have always done a semi-homemade turkey dinner -- small turkey, Stovetop Stuffing, etc. and we've always enjoyed it. Although I have to admit, the aroma of those turkeys deep frying is unbelievable!
Around the first of November, you will get more information in the mail from the resort -- the menus and some of the activities that will be scheduled. Be sure you don't miss the Turkey Bowl (touch football game) on the beach on Thanksgiving morning!!!
BTW, the local grocery stores (Publix and Harris Teeter, I'm sure of, but probably the others as well) do offer take out dinners as well. I think some of the major hotels on the island have Thanksgiving dinners or buffets as well.
Thanksgiving at the Hilton Head resort can be VERY addicting...