Comment by southern_cross

Heat dumping is done outside the room, of course, but that's a separate airflow, one that's generally disconnected from the room. The cool AC flow itself is usually a closed cycle of some sort. You would be kind of defeating the whole purpose of trying to cool and dehumidify the air if you did otherwise, plus your AC system might have to run continuously in order to get anything done. There will always be some leakage, of course.