It does appear to be possible with curl by using the -L option. This forces curl to follow the redirect. Additionally, it is important to specify an output name with a .zip extension, as the default will be a random alpha-numeric name with no extension. Finally, do not forget to add the ?dl=1 to the end of the link. Without it, curl will never reach the redirect page.
curl -L -o newName.zip https://www.dropbox.com/sh/[folderLink]?dl=1