Because of the nature of Growl, it needs to keep the WiFi radio enabled, so it will have an effect on battery life. If you have other applications running already that require use of WiFi, then the effect will be negligible, but if Growl for Android the only app on your phone that uses WiFi then the difference will be more significant.
The GNTP support in Growl for Android uses polling to subscribe to notifications from Growl for Windows every couple of minutes. If you have the "Listen automatically" option enabled (which it is by default), Growl for Android will turn itself off when you disconnect from a WiFi network, and turn itself on when you connect to another WiFi network. Changes to the polling model in future may reduce the polling rate to once every 10 or 15 minutes, but I don't imagine this will have a large impact on battery life, as it will still need the WiFi radio to remain on, it will just reduce the amount of traffic being sent and received.
By default, Android tries to turn off the WiFi radio whenever it's not in use, so it may also choose to disconnect from the WiFi network to save battery life, thereby stopping Growl for Android. There is the potential for Growl for Android to lock the WiFi radio on, thereby disabling this behaviour, but I've chosen not to implement support for using the lock at this stage.
Thanks,
Carey