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.

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.