A surge protector is not the same as a GFI. Surge protectors simply have a small fuse in them that will trip if a surge/spike comes through the line towards whatever you have plugged into it. Most UPS's have surge protectors built into them, part of being an "uninterupted power supply". If it is plugged into a GFI, I would be leary of the UPS affecting the GFI's ability to sense a fault.