[SPS-1]

Do portable air conditioners actually work?

That is a single hose air conditioner. So the answer is easier --- NO.

It has a window kit with a hose that expels hot air. But for every cubic foot of hot air that exits the house, another cubic foot of (probably hot) outside air will be sucked into the house through ever-present cracks and gaps in the house envelope. The expelled air might be hotter than the sucked in outdoor air, so there will be some net cooling, but thats a heck of an inefficient system.

 

[SPS-1]

... window air conditioners use outside air for the condensing so they don't take any air out of the room....

Plus, the heat producing pumps and motors are placed outdoors so all that electricity they use (and air conditioners use a fair amount of power) is producing heat outdoors rather than indoors.

 

[SPS-1]

You said a window unit won't fit; I wonder how small or strangely shaped your window is that no window unit will fit???

Yes. In a minute of searching, I found several window AC's that were in the range of 12" high x 16" wide.