An input terminal of Operational amplifier or Comparator installed an ESD protection diode. Could I apply an electrical current to ESD protection diode on operating it?

Operational AmplifierComparator

For IC during operation, it must not apply the electrical current for ESD protection diode.
For the IC during not operation. You can apply least electrical current of it, if you confirm to have a leak current or not for the terminal of the IC.
The function of ESD protection diode works to discharge a little bit energy like as a static electric. The ESD protection diode doesn't design suitable applying constant current for it.
In rare cases, there are products that are tolerance to passing current through from the input terminal to GND of an operational amplifier or comparator. You must design it to be lowered to the rated value or less.