The position shall be almost immediately accurate (about 2 minutes) provided it was last swiched off in the area, and the backup battery is full. In this case, your GPS shall still have the almanach and constellation for that location in memory.
If you swich off in Petaouschnok, jump in a plane and swich back on in london, it may take up to 5 minutes depending on the reception condition to rebuild the constellation data.
Having been in the Gulf and UK during the Gulf War period .... got a bit of dosh in the ol' bank for that one !!!! I can clearly state that my GPS showed very strange results ..... and I know from the military boys that we knew in the gulf confirmed the 'altering' of GPS signals then .....