Can a person with thyroid disease use the diet that dr. Oz recommend?

Take medication. You may use the diet recommended by dr. Oz, but do not go off your medication. Diet is not going to be substitute for thyroid medication.
What diet? The only part of a diet that is most important to normal thyroid function is to have sufficient iodine, which can be found in sufficient quantities in iodized salt and seafood. Don't eliminate green leafy vegetables or nuts from your diet without first consulting your physician. Most importantly, don't take medical advice from dr. Oz and other doctors who don't know your personal health history.