Lots of data is necessary to record the details of your ride, but I'm pretty sure you only get charged for internet traffic. GPS is a radio signal broadcast from a satellite constellation. Your phone is going to tap into that, record your data, and you can send it up when you're good and ready.

How often are you really going to be looking at the map while you ride? I've got a Garmin, and it's usually on the page with my speed and how long I've been out; I only check the map when I'm turned around, or want to know if it'd be a bad idea to see what's down this road.