Taking into account power factor when calculating energy savings
Neither you, nor the fan, can tell what the power factor of the site is, just by looking at the electrical socket (or however the fan connects).  The supply to the motor is an AC voltage, and the current drawn by the fan motor (and the phase relationship to voltage) is entirely dependent on the motor itself.  You are correct that you can ignore the "site power factor".

Note that reading the fan current may not tell you what you expect.  It might not change much, but the phase (and thus, the power factor) could, and that reflects the amount of actual work done by the motor.