Is it true that a remap can influence positively fuel economy?

Yes, when you compare same driving conditions from a same point A to a same point B at same driving speed. Since the torque is increased, the engine has to use less of its reserves hence less of gas to maintain a certain speed. On certain cars, the fuel savings can go down by up to 1 to 1.5L/100 Km, but on average this value is in the 0.5 to 0.8L/100Km range.