Quantum mechanics throws a tiny element of chance into the play,

QM's tiny elements of chance can be amplified as much as you like. See Feynman's Bomb

but since you have no conscious control over the quantum effects anyway

Whatever that memans. You cant predetermine an indeterministic event in your brain. but if an indteterministic event does occur in your brain it does not have to lead to action: other neural events could vote it down.