engine accelerates on its own

To be fair, if you are starting from a stop and the accelerator for whatever reason actually DID go full throttle to spin the tires, the ABS system will not engage. Also, if memory serves correctly, if you have a foot on the brake, and one on the gas then the ABS system also will not engage. Just a little FYI.

 

Regardless, when accelerating from a STOPPED position, ABS will not engage. Period. Even the old school systems. ABS will only engage if all 4 wheels are showing movement BEFORE the brake pedal is pressed, i.e. the vehicle must be already moving.