No, putting a bucket of water in a room with an air conditioner does not directly humidify the air in that room. In fact, air conditioners typically remove humidity from the air as part of the cooling process.
Air conditioners work by cooling the air through a process that involves removing heat and moisture from it. The warm air is passed over cold coils, causing the moisture in the air to condense and collect as water droplets. This condensed moisture is usually drained outside or collected in a separate container.
If you place a bucket of water in the room with the air conditioner, it will not significantly affect the humidity levels. The air conditioner's cooling process will continue to remove moisture from the air, counteracting any minimal evaporation that may occur from the bucket of water. The effect of the water bucket on the room's humidity would be negligible.
If you want to increase the humidity in a room, you would need to use a humidifier, which is specifically designed to add moisture to the air. A humidifier releases water vapor into the room, increasing the humidity levels as desired.