No, a window air conditioner cannot blow cold air out of one side and hot air out of another side at the same time to cool one room and heat another room simultaneously. Window air conditioners are designed to extract heat from the indoor air in the room where they are installed and release that heat to the outside through the condenser coils located at the back or sides of the unit.
The cooling process in a window air conditioner involves absorbing heat from the indoor air, cooling it, and then discharging the heat to the outside. It does not have a separate mechanism for generating hot air.
If you want to cool one room while heating another room, you would need two separate units: an air conditioner for cooling the room and a heater for heating the other room. Alternatively, you could consider a ductless mini-split system or a central air conditioning and heating system that allows for zoned cooling and heating, providing independent temperature control in different rooms.