That's basically how this one works, except parts are compiled as the file goes from person to person. For this song, drums were recorded, then guitar/organ on top of that track, then I added bass to the drums + guitar/organ track. Then the person after me uses my version, etc. We have been using soundcloud to share with each other because it's easy (and everyone can use their own software), but I'm sure there are plenty of other ways to go about it. It's a pretty low fi arrangement =P, but we've been having fun with it so far. You can look through the original music club tag for a better idea of how the process works.
Hmmm... So I don't really have the ability to record myself playing anything. I may be interested in taking samples that people record and mix them.... Yeah that idea sounds like a lot of fun. But I have to reach a little better level of understanding my DAW. This interaction seems promising, though.