They do.
Depending on the camera you're using you may be able to connect a wireless mic setup to it. You'd have two microphones, one on your person, one on the opponent. Some of these rigs are are pretty costly. Our gaming group started doing Battle Reports relatively recently, and I'm still researching the appropriate audio setup for us. We visit
LGS in NY Metro area, some of these places tend to get really noisy as you can hear in some of our BatReps (
www.battle-report.com) and we're realizing that we have to address the audio situation ASAP.
Cheers,
Thoth