If on a single vCenter this process works really well - just need to make sure the catalog is shared. If the new org can spin up the VM on the same datastore it will. If not the system will make a clone of the VM's to a datastore the new org has access to, then link to those.
It gets a little more complex if you have more than one vcenter - (if you need ALL the details on this please just let us know) - but the basics come down to; catalog exports cross vcenter will do an OVF export and import to make the shadow copy on the other vcenter. This is a very slow process, and in some content can change the content (IE scsi id's ect). Method do exist to avoid this OVF export if you have that issue to worry about.