Yes, evaporative air coolers can cause damp. This is because they use water to cool the air, which can lead to an increase in humidity levels. The water evaporates into the air, which can cause condensation on walls and other surfaces. This can lead to damp patches and mould growth. To prevent this, it is important to ensure that the air cooler is regularly maintained and that the water is changed regularly. Additionally, it is important to ensure that the air cooler is not placed in an area that is prone to damp, such as a basement or a room with poor ventilation.