It would be nice if it does so. I shoot a job just 2 days ago with C1Pro using Canon 5D3, then when I switch to Nikon D800E the C1Pro would require restart to be able to tether with a new camera, and the capture naming has to be reset. Unless I was missing something, at least for C1Pro it is not yet support. It would be nice if hey do, or even do it wirelessly, common, it is 2012!
This is unique to Nikon+Canon in Capture One. Nikon's new SDK (updated for the D800) interferes with Canon's SDK. In previous versions of C1 (e.g. 6.4.2) you could connect a 5D2 and a Nikon camera and switch back and forth without restarting.
In Capture One 6.4.3 you can still connect e.g. a Canon and a Phase One back and switch back and forth between them without restarting the software or disconnecting/reconnecting the cameras. You cannot, however, shoot both at the exact same time - you must pull down the camera selector to select Canon or Phase or Mamiya Leaf etc.
This works well for applications like the photographer shooting some safety shots with a Canon and then switching to a Phase back for the real shots (the digi tech or photographer can simply select the other camera). But it would not work for synchronized shooting (e.g. stereoscopic images of a moving subject). For that you'd need to have two different computers - each handling one camera. However, you could set up a relatively easy script to transfer all new captures from the one computer to the other computer, which, in "hot folder" mode would see them (side-by-side with it's own camera's images) a few seconds after the shot was taken.