This is actually something that me and My friends have been doing on and off in our 'wierd weekends' for many years.
A looooong time ago we here in Melbourne has a theatre troupe called "double Take" who usedto tour around the fringe theatres (ie, Astoria, Valhalla etc) and on the screen they would play a movie, but the 'troupe' would be on the stage in front of the screen and would dub the voices, sound effects, even the soundtrack LIVE every night.
Because they did it live it was always different, and if was a brilliant experience. It was almost always sellout every night they played. SOme patrons actually going to the same movie more tan once just to see what the troupe would dub differently.
They actually released a OAV that was the same thing, but it just want the same not seeing them there live. Its an hilarious re-dubbing. One of their best. The 'live' shows were about more than just the dubbed quality tho. Some of the funniest things were when they made mistakes and they tried to cover it up, yet STILL keep it matching the movie haha..

Good times.
Of course, once we had seen this a few times (My friends usedto frequent the Valhalla theatre as often as we could. It was more than just a movie theatre.) we decided "hey.. we can do that too!" so on weekends we used to gather at a house somewhere and take our favorite movies and just watch them with the sound turned down and add in out own stuff.
We did to this for a few anime's (we all were into anime) and the best one we ever did was dubbing GOLGO 13. Man, we totally excelled ourselves doing that one. Its a bit of a pitty really because after that one we all kept trying to 'beat' it, and as we couldnt get any others as histerical we sort of just stopped doing it.
I have never actually thought of doing this with microphones and recording it tho. It would be VERY interesting to see what some people could come up with trying this.
If I could work out how to do it on PC I would definately give it a shot myself.