The ESD protection structures on all inputs and outputs for the ispPAC-POWR1014 or ispPAC-POWR1220 are designed to be 'hot-swap' compliant, so that signals can be applied to them without drawing excessive current or inadvertently powering up the device. So, no, you cannot power up an ispPAC-POWR1014 or ispPAC-POWR1220 through the ESD protection diodes.
While you cannot power up the device through the inputs or the outputs, the VMON input pins have a 60k (nominal) input impedance to ground, so applying signals to them when the device is either powered or unpowered will result in input currents of less than 100uA per pin. These input currents, however, are unrelated to the ESD structures, are returned to ground and will not cause the device to power-up.