Laryngeal nerve palsy or paralysis of the nerve to your vocal cords is usually a temporary problem after this type of surgery. You should regain the full use of your voice in the first few days. In some cases the temporary paralysis lasts much longer from days to weeks.
In a very small number of people permanent paralysis occurs. When the surgeon fuses the spine anteriorly the trachea and soft tissues of the neck must be moved gently out of the way. The doctor finds the laryngeal nerve and carefully moves it to the side to avoid cutting it when opening the neck.
In some people the nerve is hard to find and gets nicked during the incision. In another small group there is an extra branch of the nerve that is too small to see easily. If this gets cut but the main branch remains intact, then some partial paralysis occurs. In most cases the condition is usually temporary.
With nerve damage there's no quick and easy way to know what the long-term picture will be. It's usually a wait-and-see affair. First you wait and see if you are in the group that recovers in a day or two. If not, then you may expect recovery to occur in the first two weeks to two months after the operation. Permanent nerve damage can occur.