This really depends on how the directory structure is set up at the location you are moving the files to, compared to where they are coming from.
SolidWorks Explorer is good at copying a top-level file (drawing or assembly) and all of it's children, but you get to send the parent to one location and all children to one location. If the children need to be scattered to various directories, it can be a real pain. It also does not get drawings of the children. They must be copied seperatly. If they are going to the same directory as file they are referencing you will not have any problem.
If the directory structure will be the same at the destination as it is currently, just a different root structure, you should be able to move the entire structure in windows explorer. SolidWorks looks at a relative path before it looks at the absolute path. (go to the help file and search on "referenced documents")