The GPS will be turned off when the device sleeps. This will happen sometime after the screen turns off. You can take a PartialWakeLock with PhoneWakeState however it will have a bad effect on the battery.
You can also use StartServiceAt to wake the device every x minutes, wait for a GPS fix and store the coordinates. You can call CallSubDelayed to send the coordinates to the activity. Once the activity resumes it will handle the call sub message.