Is a turkey safe to cook and eat if it has been defrosting in refrigerator for 1 week?

It is not safe to eat.

According to the USDA, a frozen turkey can be kept in the refrigerator for no longer than 2 days before cooking. After that, the turkey will begin to spoil and develop harmful bacteria. To ensure that the turkey is safe to eat, it is best to cook it within 2 days of thawing it in the refrigerator.

If you are unsure whether or not a turkey has been properly defrosted, it is best to err on the side of caution and discard it.