Actually, it *might* be possible. Maybe. Distant chance.
On a 3-pin TRS mic connector, it would likely not work because the power for an electret (cheap) mic capsule is on a dedicated pin, and there's nothing else for that connector to do anyway.
On a 4-pin TRRS headset connector, the mic is "phantom powered" with 5 volts through a 2 kohm resistor, on the same wire that the signal comes back on. This allows some basic detection of what type of device is plugged in, and some other functions by that button:
- Open-circuit (5v) = nothing plugged in.
- ~2kohms to ground (signal centered on ~2.5v) = headset with mic.
- Continuous short to ground (0v) = headphones with no mic.
- Momentary short to ground (0v) = button press.
- Careful design of how strongly it's pulled to ground by different buttons (different resistor for each, not quite 0v by different amounts), can differentiate them too.
Note that the button disables the mic (shorts it to ground) while it's pressed. So you can't hold it for PTT. But you *can*, possibly, in theory, detect a momentary button press, let the wire stabilize again, and then use the mic. You'd also need a slight delay to be able to detect the loud pop that the button causes when you press it, and kill the delayed signal before the pop gets all the way through the delay.
I haven't seen any ready-made software that does that on a PC, but that doesn't mean it doesn't exist.