If you are able to find your parts and do a test go for it, but I wouldn't spend any money on anything with the word "bluetooth" in the description, unless you have another reason to own it (like a cellphone etc). Even a bluetooth headset (headsets are best for filtering out unwanted noise) is more or less useless for speech recognition using the windows engine. Dragon is supposed to support bluetooth but reports are still generally not great, and of course dragon is expensive and Vox doesn't work with it.
Still you never know there may be a bluetooth device out there that works well, and if anyone finds it I'm "all ears"...
It does make me think tough, I wonder about some kind of wired (or possibly RF) intercom system. I have no idea what they would cost new, but you could probably pick something up second hand on the cheap.