Hi mark,
Yes, you need to run SE06 even after completion of system copy as it enables you to perform following functions as post installation actions:-
1. Generating basic settings of change and transport organizer .
2. Closing other open requests & tasks.
3. System change settings.
For more information, you check http://itsiti.com/se06-processing-after-installation-of-cto link.
Regards,
Nilutpal.