The GM HEI module is no different than the mopar ECU, it is a switch to ground that opens and causes the magnetic field in the coil primary to collapse and creat the high voltage in the secondaries. The module itself may draw 5-7 amps which I am quite sure the mopar ECU does also but the power to operate it does not go through the ballast. The ballast is to limit the current flow through the coil.
GM did not use a ballast but they also designed the coil it to operate without one. If you use a stock mopar coil or an after market coil that is designed to be used with a ballast without a ballast you will allow to much current to flow through the coil causing it to run hot at low rpm's shortening it's life expectancy. This is true whether it is a GM or mopar ECU. The original poster is just replacing the mopar ecu with the GM HEI module, no mention of using a HEI compatible coil and from the picture he later posted it looks like an Accel Super Coil which is designed to be used with a ballast.
A ballast resistor by definition is a variable resistor where the resistance increases as it gets hot. This characteristic limits the current flow through the resistor. It is also this characteristic that allows more current flow at high rpms, because it does not get as hot, to offset the natural drop off in the coils output do to the decreasing time current is flowing through the primaries. It also allows for completely bypassing the resistor in the start mode to get more output from the coil when starting the engine.