No, that would be wrong for two reasons. They would not be the same div, regardless of name, and id's are supposed to be unique, not appearing more than once on a page. #productDescription is properly only the description content.

You can make a new <div id="productDescriptionWrapper"> above the beginning of the description code block, with a </div> to close it below the last of the elements you want to enclose.

Then you can change the styling of #productDescriptionWrapper which is already in your stylesheet.