I think No.
The green wire (On / Standby) is a logic input to the switcher control chip or maybe the power factor corrector. The circuit often has a capacitor on it for soft start. It has a response time measured in large fractions of a second. This will not take a PWM signal.
Also, as with most low cost multi-output switchers, the "main" output probably has a minimum load requirement, needed to stabilize the magnetics. In your case, it is the +5 V output. If it has zero or a very low load, the +12 V output might not be well regulated. Of course your results may vary, but I've ridden the ATX wave from the beginning, and despite there being many instructional videos about turning one into a bench supply, lab supply, etc., they do not make good general-purpose supplies. They are designed and tweaked from the ground up to do one thing only, power a motherboard (seen as a capacitive and/or resistive load) for the absolute lowest possible installed cost. Outside of that, all bets are off.
ak