Probably not. In a recent study of 382 operations like yours, only nine patients (2.7 percent) had any hoarseness after surgery. And only two of these patients had problems that lasted more than three months.
Doctors used to think there was a greater risk of hurting the nerve that goes to the vocal cords if surgery was done on the right side of the neck. Right-sided surgery was believed to endanger the recurrent laryngeal nerve, which hooks up with the voice box (larynx). Research now suggests that the risk for injuring this nerve is minimal and is the same for both right- and left-sided surgeries. If you have any voice changes after surgery, they'll likely be subtle and short-lived.