Mobile Tethered Video Shooting
I have personal experience with tethered shooting for different purposes, and I have absolutely NOTHING to say to dissuade you. 

Having said that, there are some things about which you need to be cautious. I don't know what your end result is going to be. Is this going to be a webcast? or are you trying to save some post-production time on a movie for distribution? That makes a huge difference in what you need to watch out for. Without that, the best I can do are some very broad generalities.

First, prosumer cameras take up a lot of bandwidth. Do some tests to make sure your hard drive spins fast enough to capture the data coming down the wire. I had to upgrade to a 10k RPM hard drive for a stright-to-disc project once. Use lower quality cameras for less bandwidth, but few of those have HDMI.

Second, depending on what you're doing for VisFX, coupled with the complexity of the image you're using, you'll want to make sure that your processor is fast enough to render everything on the fly. That's a total crapshoot...but VisFX on a relatively static talking head will take less processing overhead than VisFX on a scene with fifteen people all moving in front of the camera.

Third, if you're webcasting, see my bandwidth comment above. You've got similar issues on the output side, and you'll need to render your output to be small enough to be web-friendly. Uncompressed AVI to compressed QuickTime, Flash Video, Windows Media, etc. takes time and processing power. If this is the plan, you may wish to consider a dedicated machine that transcodes for web in realtime. The ones I've used are dedicated machines, I'm not sure if they'd play nicely with your system.  

You have a lot of variables at play here. Before you invest in the gear, I would recommend borrowing and renting what you can, and testing the bejeebers out of the system to make sure it's doing what you need. If something doesn't work, figure out that smaller piece of the process, then move on. I can guarantee that by doing it and asking questions along the way, you'll lern more about doing this than you ever wanted to. 

But I'm definitely NOT dissuading you. Be excited about your journey into new technological realms, and go for it!

Good luck!