There’s no point as a swamp cooler does not have heat to reject. A heat pump in a traditional AC works by making one side hot (outside) and one side cool (inside). A swamp cooler decreases temps by evaporating water, which absorbs energy.

Also, swamp coolers are only effective in very dry environments. Unless you’re in the desert it’s going to make it feel warmer by raising humidity significantly. A large part of why AC makes it feel nicer is reducing humidity, which allows sweat to work better.

Swamp coolers increase humidity not decrease it. You put water into them and the vapor goes into the air. AC is the opposite, it condenses water from the air and that’s why the drip tube is there.

The window hose is for exhausting hot air outside.

Swamp coolers are designed to exhaust cool wet air indoors.

Just park your swamp cooler in front of an open window or patio door. Increase air flow throughout the house with fans. Open upstairs windows to create a cross breeze to move out hot air that naturally convects, and crack downstairs windows to help vent out the increased moisture. It sounds counterintuitive, but you are not supposed to seal your house up like with AC. You want outside air coming in to vent out the humidity

I suppose you could get a hose and connect it to the cooler and window. With a fan (blowing in), you would get cooler, wetter outdoor air.

Swamp cooler cools air by evaporating water which uses up the heat energy in the room. Air conditioner on the other hand takes the heat energy from inside and moves it outside. They work by a different principle. A swamp cooler with an exhaust went wouldn’t work because you’d then just be pulling in hot replacment air from somewhere else.