If a laurel hedge has been heavily trimmed(Exposing bare wooden branches)
will it ever recover?
Yes, it will recover, it will take it's time but by next summer you will have thick bushy growth covering the branches - then keep it in check by a regular light trim each summer. It will look better if you can do this with secateurs or hand shears, removing individual shoots, rather than with a hedge trimmer that will cut through the large leaves and leave you with ragged edges that turn brown and look untidy. But of course if it's a huge hedge then it may take much too long to do it the slow way.
But don't worry, providing your hedge is established and healthy in other respects it will recover well.