No.
Thyroid function tests are often "messed up" in critically ill patients and these results often have no clinical significance. This phenomenom is called nonthyroidal illness or sick euthyroid syndrome.
Consider thyroid function testing only when there is super high clinical concern for thyroid dysfunction ie myxedema coma or hyperthyroid storm. Even in these cases however, treatment should be initiated based on clinical presentation and severity of illness, not on the results of thyroid function tests which may take hours to result.
Source
Irwin & Rippe's Intensive Care Medicine, 5th ed.
Sabatine, M. Pocket Medicine: The Massachusetts General Hospital Handbook of Internal Medicine. 3rd ed.