It absolutely would help the temperature of all of those. Additional airflow will increase the heat rejection of any heat exchanger, particularly the tube and fin or plate and fin variety.
The air leaving the first exchanger and going past the second will also be cooler while simulaneously having more volume, so any second row exchangers (condenser) and especially third row (radiator) will see significantly improved efficiency.
The fluid leaving any of those exchangers will be significantly cooler. Under-hood temps will also be significantly lowered. It will not over-cool the engine, because the thermostat controls flow. But it will vastly increase the maximum heat rejection rate, and any coolant leaving the radiator and entering the engine will be colder.
You might run a slight risk of over-cooling the transmission or power steering in very cold climates, but a piece of cardboard would instantly solve that. The fan clutch doesn’t engage at low temps anyways, so the CFM increase at cold temperatures isn’t very much.
I would expect you would see the most drastic improvements in very hot temperatures, low speeds, low-mid engine RPMs, and high torque demands, which sounds like the conditions you describe.
Cost for the Explorer fan and HD clutch is about $90-100. Very easy install. You will need a 36 mm wrench or adjustable wrench, maybe a fan clutch holding tool, a 10mm to remove and reinstall the shroud.
The Explorer fan and clutch can be installed and removed with the shroud in place. Not sure about the factory fan.