Yes, but the recirculation fan(s) move air from the lining
back to the cabin. So if the air in the lining is heated by the exhaust from the equipment cooling and we are then move it back to the cabin, are we then also removing heat in the process for the benefit of the passenger cabin?
Obviously, if we remove air from the lining to the cabin, more air will flow from the cabin to the lining as well. So the question is which air source is warmer. The air coming from the exhaust from the equipment cooling or air from the passenger cabin.
Hence, would the air in the lining be warner if it wasn't recirculated.
Regarding pressure:
A pressure equalization valve is in the aft bulkhead of each compartment. The valves let only enough air flow into or out of the cargo compartments to keep the pressures nearly the same as the cabin pressure.
It was just a few lines lower than what you quoted above.
So even with a leaking seal in the door, air should flow through the pressure equalization valve.