Yes. in fact , as the 3.3v pin still has power. The GPS will be fully on and will not need to use the supercap.
If you do turn it off completely.. the longer you wait to turn it back on, the longer the fix will take as the ephemeris (true orbit) being held in the SuperCap will be older.
BTW: if you need to get a fix in seconds… no matter how long the device was off, this can be done using the BerryGPS-GSM, which supports assisted GPS.
Mark --OzzMaker.com --