I presume that you're referring to the GPS going off when the screen goes off... putting the meat into a SERVICE and holding a PARTIAL_WAKE_LOCK (screen and keyboard allowed to shut off, everything else keeps on at full power) should keep the GPS running.
No. The GPS works fine with the screen off. The TelephonyManager stops updating its signal strength when the screen is off. You need a full wakelock (not the SCREEN_BRIGHT one, but the one just below that) to get signal strength updates.
Believe me, if this would work without the screen on, I wouldn't require it