Yes that is exactly what is happening.
My question is will the holley have the same trouble?
Yes.
I take issue with your characterization of this situation as "trouble" on the feet of the ECM. You're trying to start a car with a dead battery. That's bad for the battery and the electronics, and if it starts it becomes bad for the alternator. Don't do that.
Here's the deal, electrical components consume watts to operate. Watts are delivered as a function of voltage and amperage. If the voltage goes down, the amperage to supply the necessary wattage goes up. Amps are what generate heat in a conductor as the current flows through it. It's what blows fuses. The conductor melts
Trying to start a car at 10v instead of 13.5 results in a larger current draw (35%!) to power all these things, which starts cooking stuff. Specific example: If your fuel pump needs 100watts to operate at a level sufficient to pressurize the rail and let the car idle, it'll pull 7.4 amps at 13.5V. But at 10V? The draw becomes 10 amps.
Translate that to modern ECMs that have overcurrent protection, and they just won't work below a certain voltage. All those electronics packed into that box cannot run at those kinds of current levels without melting stuff, so they're designed not to.
So don't do that.
Get a new battery and put it on a tender when you're not driving the car.