The physics is simple.
If the hose is of the proper diameter for the flow rate generated by the pump, then the pressure at the pump will be about equal to the vertical distance (the height) between the pump and the point where the water becomes free-flowing, times a density value of about .45 PSI/ft (which is derived from the weight of a cubic foot of water divided by 144 to convert from square feet to square inches). If you are pumping the water to the top of the barrel and letting it fall, then that would be the height difference between the pump and the top of the barrel. If you are pumping the water into the bottom bung, then you would use the height difference between the pump and the top of the water in the barrel.
Therefore, the pump would encounter slightly less pressure if the tank were filled through the bottom bung, at least until it became nearly full. The difference is small enough that it would make only a small change in the amount of time it would take to fill the tank.
The fact that there may be several hundred pounds of water in the barrel is immaterial, since pressure is pounds per square inch. You could calculate the pressure at the bottom of the barrel by dividing the weight of the water in the barrel by the area of the barrel head in square inches (assuming straight sides, for a wooden barrel you would have to use an average diameter to get an exact figure).
Bartolomeo