I designed a full duplex headset for 4 users using throat-microphone with squelch, AGC and headset for wind-positive pressurized air suits in the 70's for low level nuclear service in maintenance of 2ndary heat exchangers. These were all conducted on a shared single wire pair without echoes for excess sidetone.
I have left out a few details on sidetone cancellation, but characterizing the coughs , pops and noise from the audio, is a matter of spectrum analysis to detect the best SNR trigger that begins with true speech. A cough is noise and a throat mic has very insensitive to medium and high frequency yet very sensitive to low frequency such as a cough. So detecting bass impulse noise like a pop or cough is good for detection, but then use a mid-range bandpass filter to attenuate that noise. This will improve the poor quality of throat microphones immensely.
So a precise answer without precise headset specs is impossible.
If you get stuck "a little cough" is a good way to trigger the mic ON in exceptionally noisy environments.
Forget about impedance matching for audio electrical impedance.
- ** Pay attention to matching frequency spectrum for band pass, band stop and trigger matching..**
You only need to consider mic gain, speaker damping factor and amplifying to match the signal/noise ratio spectrum. ie match receiver theory
Forgive me on details, I designed it 45 yrs ago.