"This leads me to conclude that the maximum current draw for the Arduino must only be 200 mA. "
Why? You can draw 500mA from the USB connector. It provides current in parallel to:
the 5V header pin
the 16U2
the 4 VCC pins of the 2560
the 5V to 3V regulator
the op amp that does auto power switching
the 5V on the ICSP header
So if current comes from the USB port, the Arduino is limited to 500mA.
If current comes from the barrel jack, the Arduino is limited to 1A.
If current is supplied to the board via the 5V power header, you bypass the reverse protection diode and the Arduino is limited to what the pin will support before it melts.