No reason a wireless headset wouldn't work, if it presents itself as a recording device.
For that model in particular,
audio quality seems OK. Like most cheaper headset microphones it sounds a bit "woolly". It does pick up puffs of air in the video, but that can usually be mitigated by repositioning the microphone.
Reviews imply the battery life is on the low end, and that it's probably not the most reliable(connection issues, battery stops charging altogether, microphone stops working, etc...), so YMMV.
This is my personal, biased opinion, but I don't buy logitech products anymore; The hardware is mediocre for the price, and the software can be downright abysmal.
The top comment on
this Youtube video(which doesn't bother to include a recording of the headset mic
) does suggest it has a "hidden" bluetooth feature:
Here is what to do.
1. Open your computer, laptop or net book. Look for the bluetooth menu and select bluetooth.
2. Have the bluetooth window up and have it search for new blue tooth devices.
3. Turn on the H600 power.
3. Hold down the mute button on the headset at the same press and hold the + volume power button on the headset. The volume Up + is located on the right side of the headset (microphone side) at the top of the blue ring.
The green light will start to flash steady and then start to flash faster.
You will see on the computer's blue tooth window it will say "searching for new bluetooth devices. As soon as as it finds the H600 it will appear and pare up with the H600. Release the mute and volume up + button.
You have added bluetooth feature to the H600.
It is now a H800.
Though it's of course unsupported by the manufacturer, so no telling how well that works.