If there is no electricity, running a window air conditioner (AC) will not hurt the AC unit itself because it won't be receiving any power. However, if you attempt to run the AC without electricity, it won't provide any cooling effect as the compressor and other components that require electricity to function will not work.
It's important to note that running an air conditioner without electricity is not advisable and won't achieve any cooling. In fact, attempting to do so might lead to unnecessary wear on the AC's mechanical components and may void any warranty it has. Additionally, if you try to run the AC using a generator or an alternative power source not designed to handle its electrical load, it can damage the generator or cause other electrical issues.
If you are experiencing a power outage and want to protect your air conditioner, it's best to turn it off completely until the electricity is restored.