Yes. Using pins 7 & 8 in this way (pair 4 of an ethernet connector) would almost surely guarantee damage to the Ethernet magnetics and associated traces. Unless the device only works at 10/100 BaseT speeds (which does not use, need, or require this pair) there is very little a designer can do to avoid such damage and still remain within Ethernet specifications.
In the unlikely case that the designer chose to add TVS diodes on the field side of the magnetics, which is generally not recommended as this counterintuitively would tend to reduce ESD reliability and degrades signal integrity, you would destroy these diodes together with the magnetics.
Of course that depends on how much current the power supply can provide, but for the sturdier PoE magnetics, a maximum of 350mA for common-mode current in a pair is the maximum specification but the differential mode is normally specified at less than 10mA. Given the <2Ω winding DC impedance, you could be talking as much as 12A going through the magnetics.
Using whole pairs instead (e.g., 7&8 for Vdd- and 4&5 for Vdd+) is closer to the normal way for PoE devices to transfer power (PoE 10/100 mode B) and, if the device is new enough, these common modes are isolated by capacitors in the RJ-45 magnetic jack or in components associate with discrete magnetics.
But the damage will mostly be relegated just to the RJ-45 jack, or to the jack, magnetics, and associated PCB traces--if using discrete magnetics. Any transients that make it to the other side of the magnetics are unlikely to transfer enough power to destroy the ESD-protection diodes in the PHY ICs.