No, a grounded adapter will not allow a 115V air conditioner to function properly. The voltage rating of an appliance, such as an air conditioner, is specific to its electrical requirements and must match the power supply it is connected to.
In most countries, standard power outlets provide either 110-120 volts (such as in the United States) or 220-240 volts (such as in many European countries). Adapters that only modify the physical shape of the plug or provide grounding capabilities do not change the voltage of the power supply.
If you have a 115V air conditioner and the power supply in your location provides a different voltage, you would need a voltage converter or a new air conditioner compatible with the available voltage. It is important to match the voltage requirements of your appliance to the voltage supplied by the electrical system to ensure safe and proper operation.