GFCI (Ground Fault Current Interrupt) outlets will make no difference.
GFCIs are designed to trip, in case you happen to be in contact with the live wire, while touching a ground (like, a metal sink). Neither happens in the normal operation of any charger.
The safety of charging cells comes mostly from the charger, and how you operate it.
-If your charger is capable of overcharging a cell, then you have the wrong charger; there's no reason, in this day and age, to not use a charger with an auto shut-off.
-Proper charging would require that you put the charger in a charging bag; not because of a possible overload, but in the eventuality that the cell has been physically damaged; it may vent out during charge.
You do well not to leave it unattended. Using a charging bag would let you get out of the house, as long as the bag is properly flame resistant, and sitting on a non-flammable surface, with no flammable elements around it. When a damaged battery vents out, it could be smooth, or very violent; they can easily fly across a room.