I checked the API pages of file_directory_path() and file_create_path() just to be sure, and it looks like they return relative paths. This should make $local_path relative to either the files/ directory, or the Drupal root directory.

It may not be clear from the documentation, but $image_path is supposed to be an absolute path pointing to an image resource, typically from whatever system had the images in the first place. The importer copies the image from $image_path to $local_path if the file doesn't exist locally.