In most cases the impact will be negligible; it will be slightly lower if the user already has other apps using GPS, and slightly higher if a large number of geofences are defined.
We use Apple’s CoreLocation and Google Play Service’s geofencing capabilities under the hood to ensure we allow the phone to batch GPS requests when necessary and to use lower power mode when battery life might be needed. We never explicitly request a GPS update and only make background network requests once a day.
To get a better background on Places & geofences read up on it here as well as more information on Messaging with Places.