I would think the dressing would be soupy and awfully fat if cooked together, however, I do make crockpot dressing for the holidays, and it is excellent. Maybe cook the chicken one day and refrigerate, then cook the dressing the next day and add the cooked chicken for the last hour.
I always cook the turkey (or chicken) ahead and cut it off the bone, because I serve it on a platter anyway. It sure improves my ability to get everything done and on the table hot and at the same time. The portrait of Thanksgiving with all the dishes on the table and dad bringing in the 40 lb bird in to be carved at the table is beautiful, but as a practical woman, congealed mashed potatoes is very unappealing. By the time you finish carving enough to serve the table, everything else is stone cold. Norman Rockwell obviously didn't do the cooking...