Can you use a window air conditioning unit in a room that does not have windows and just put it on a counter?

There are A/C units available that do not require window installations, they are stand alone units. If you have a window unit and use it on a counter, you will not only have a flood (condensation)but you will notice that the back of the air conditioner is very hot, thus heating the air that you are trying to cool. It will work for a bit but you will eventually reach a plateau where the air will not get cooler.

A portable A/C needs an exhaust pipe to expel the heat and condensate out of the room.

If you put a window A/C unit on a counter, not only will you get a pool of water, the room temperature will increase as the only thing being added to the room is heat in the form of electricity. An A/C unit works by moving heat from one place (the room) to another place (outdoors). In doing this work, it uses electricity that is given off as additional heat. If the entire unit is inside the room, it will move heat from one side of the room to the other, but because of the added energy, the average room temperature will continue to increase to the point where the heat transfer out of the room through walls is equal to the electricity coming into the room. That will not happen until the room temperature is higher than that of the adjoining rooms.