Depends on your plan with the service provider and whether you
1) make or take any phone calls - or
2) use any apps (browser, video, games, etc.) that require data connection - or
3) use any sort of messaging application (some use SMS, some use data)...
If the smartphone is on but not used and the apps that track your location are in "only when in use" mode, there will be no voice, data or SMS charges.