Is it necessary to perform a loop-back test after first installing the system?
No. The loop-back procedure is a troubleshooting aid/procedure to help one determine if serial communication between the PC and Arduino board is working or not working in a typical arduino installation. It does no harm to run it on a working system, and it would probably be best to learn to run it on a working system before having a problem to prevent false positive (or is it false negative?) testing results.
Lefty