If you wish to register the software once and have it pre-registered on network machines, then you may installit on one system, activate the license there and then copy the shared folder above across different systems.

In order to minimize program's need for map data from Internet you need to ensure that the additional 2 discs of data have been installed (their contents is installed in the shared directories above). Then you may disable network connection of The Layered Earth by going to File->Preferences->General and unchecking "Stream data from internet when available". You don't have to do this for every system as TLE properties are located in

Vista or Windows 7:
C:\Users\<username>\AppData\Roaming\Simulation Curriculum\The Layered Earth

Windows XP:
C:\Documents and Settings\<username>\Application Data\Simulation Curriculum\The Layered Earth

Therefore, once you set it up on one machine, you could propagate program preferences to accounts on all other systems.