AirDroid will not drain extra battery of the device. The battery consumption is decided by device model, ROM and how you use AirDroid.
If you want to save power, you may go to Settings of AirDroid app on your phone, turn on Power saving mode and turn off Keep screen awake. But with Power saving mode on, the connection between your device and web browser will be interrupted after about 30 mins' inactivity. And the network connection may be cut off when screen goes off for some devices.
Note: Using Camera feature on AirDroid Web or AirMirror on AirDroid Win/Mac will drain the battery.
If you want to save power, you may go to Settings of AirDroid app on your phone, turn on Power saving mode and turn off Keep screen awake. But with Power saving mode on, the connection between your device and web browser will be interrupted after about 30 mins' inactivity. And the network connection may be cut off when screen goes off for some devices.
Note: Using Camera feature on AirDroid Web or AirMirror on AirDroid Win/Mac will drain the battery.