Yes. The underdash harness on an SS car is different than a nonSS car. The main issue is the instrument wiring since the SS has gauges and the nonSS has idiot lights (for water T, oil P, and amps). You will also need a different engine harness and an electrical shunt that mounts near the voltage regulator. I imagine that you could also modify the harnesses you have now with a bit of careful planning.
The shunt has to be part of the circuit for the ammeter used on SS cars. Chevy2only and others sell them. Since the shunt is located in the engine compartment, the engine harness will have the wiring for it. If you check the Chevy2only website you will find two engine harnesses, one for SS and one for nonSS.