My Garmin aircraft GPS495 will run on any voltage between 7.5V and 35V; it has an internal switching power supply. Since it is a switcher, the current at 35V is about 1/4 of what it would be at 7V, so the efficiency is always high..Check if yours has a wide input voltage tolerance.
I think it is a really bad idea to "tap" any battery bank of like cells. Even if your GPS won't tolerate the higher voltage, why not use an efficient buck down-converter to run it off the 5 cell voltage. I have several old automotive cell phone chargers that use a switcher to convert 12V to 5V @ ~300mA. They are about 85% efficient, and could easily be hacked to get 3.7V instead of 5V.