If you have a shared file system (eg NFS) then ideally you can reference backup pieces etc without having to move them. Otherwise, yes, they'll need to be made available to the restoration server in some way.
If the catalog is global, then you might need need to register the pieces again.
Here's a an example of a restoration to a new server under that assumption
http://www.dbasupport.com/forums/showthread.php?60006-Restore-RMAN-full-backup-to-different-server-with-other-name