So, going though your questions as I see them one-by-one:

"Assuming LOW was OFF?", why? - the inputs to the controller are designed to sink current - examine the functional schematic in the manual - the cathode of the LED/Opto-Isolator is presented at the signal input. Connecting this to ground (through a switch, or an open-collector output from a motion controller) allows current through the LED and the input is considered "active" (or "On").

"Not flip it on and off to reset the counter?" Think of what is being attempted here. You have a servo that you're commissioning, from power-up you might justifiably expect the deviation counter to be reset... of course, any movement of the spindle would "clock" the deviation counter. If you didn't clear the deviation counter then the servo controller could either enter the Alarm-phase, or spin the servo unexpectedly to recover the servo position. Read page 19 - function of "CL" - when "Low" (active) - this clears the deviation counter and inhibits the servo position pulse inputs. Implicitly on transition to High / open circuit, those inputs are enabled. So, all this is saying is, start with the CL input low to ensure that the deviation counter is clear. Once you're ready to test the servo then de-assert the CLear input and off you go. It's up to you to decide how to use this input in future - it could be that you want to wire-or (connect each of the servo driver's inputs) together and wire to a motion controller OC output, tied to a button on the UI. I'm a long way from my two machines with servos to check, but I'm 99% convinced that I've left these inputs unconnected (caveated by I'm running my servos as spindles, not axis motion),

"Do I have to run...." - understand the purpose of this clear-deviation counter signal (and the deviation counter), and answer that question for yourself.