No, lowering your thermostat does not make your air conditioner cool faster. The air conditioner's cooling speed primarily depends on its capacity and efficiency, which is determined by the model and size of the unit, as well as the temperature difference between the desired indoor temperature and the current indoor temperature.
Lowering the thermostat simply sets the target temperature for your air conditioner. Once the indoor temperature reaches the set point, the air conditioner will work to maintain that temperature. The cooling process will generally occur at a relatively constant rate, regardless of whether you set the thermostat a few degrees lower than the current temperature or several degrees lower.
Setting the thermostat too low can actually lead to overcooling, resulting in wasted energy and higher electricity bills. It's generally recommended to set your thermostat to a comfortable temperature and allow the air conditioner to work gradually to reach that point. If you want to save energy, consider setting the thermostat to a slightly higher temperature or using a programmable thermostat to adjust temperatures based on your daily schedule. Additionally, ensuring your home is well-insulated and using fans to circulate cool air can help improve cooling efficiency.