Thanks, Eric. Because I anticipated that the best and most appropriate response to my post would be, as you said, to try it and see, I did just that. I was hoping that when the it was connected that the crossover only affected the frequency at which point the sub was activated and the main speakers would receive a signal as a simple pass through. I still don't know whether that's the case but, even though my ability to discern subtle sonic variations , there was a reduction of sound quality that even I could tell. This was the case no matter if the crossover was in the circuit or bypassed, whether the sub's amp was on or off, its volume was set to zero, regardless of the crossover setting or if the sub is plugged in or not.
So, I got my answer, the sound is better without it. Whether the culprit is nothing more than that caused by additional connection interfaces or something a little more involved, makes no difference; it just doesn't work for me. Thanks again for your response.