Jeff,
Dragon works great with Compendium! Obviously the real timesaver is an adding definitions to the nodes. And from my point of view that is hyper-critical because that really is the documented rationalization for an argument. That is also the mechanical step that adds the most lag to the facilitation process.
Here are some observations to get you started.
You can buy Dragon Pro at Amazon for $140. But buyer beware. The $50 rebate is a bait and switch. That is for existing owners only who want to upgrade. The lack of clarity on the page cost me $100, because I bought both my brother and myself a copy assuming I would get $100 back. (The bastards)
A mechanical point I first wrestled with is turning the microphone on and off when I am facilitating. Which is obviously important because I do not want to capture my dialogue as I am conversing with the group. The spoken commands to manage the microphone are somewhat obtrusive, "go to sleep", "wake up". However, I found that the accounting plus sign on a full-size keyboard is a hotkey to turn the microphone on and off. So I can toggle the microphone silently.
Dragon will insert nodes directly onto the canvas using Compendium hotkey equivalents. Unfortunately for me, it does not properly recognize "D" for Decision and "M" for Map. However there is a Dragon solution for that too. You merely have to preface the keyboard letter with the words "Press" or "Type" and Dragon assumes that you are doing a by-key insertion, so will insert a proper node. If you experiment, you can determine which nodes insert properly with just the spoken letter and which need the keyword preface.
I am only a modest Compendium user, and have not really thought much about a way to verbally connect nodes. So I am still tethered to keyboard. But I don't really think there is a way to totally disengage from it anyway. However, Dragon does give you better connectivity with your group using any electronic facilitation tool that Dragon may recognize. I think the best voice/keyboard integration is probably facilitator-specific.
Dragon does train up on your voice pretty quickly. But if you are working with a client who has a domain specific vocabulary, you would want to have the client e-mail you any special nomenclature and acronyms before your session. Then you could insert the new words in your vocabulary with your voice prior to the meeting. That does not take long.
The microphone that comes with the software is an analog type and clearly visible. There are less visible ones available on-line with USB connections that are also more accurate. But they are significantly more expensive.
So to close, given that you are a quasi-academic (And I won't hold that against you.), I would recommend buying Dragon just for your regular day to day professional activities. And then once you've trained it up sufficiently, test it out with Compendium. I think that you will find that it can be an excellent support tool for your facilitation exercises. Jeff If you do buy it, please let me know how it works for you, because I am curious.
Steve