Well -- nobody else is offering any reply on this -- so I've managed to figure it out myself. The answer is Yes, you can remove the lever from the body (I would have been seriously surprised if something from Campy wasn't re-buildable).
So for anyone else who wants to know, here's how to do it.
first off, it is a little different than on the Nuovo Record/Super Record levers -- with those, you loosen a small grub screw inside the lever body, and the hinge pin simply slides out and the lever can be removed easily. With the C Record (also Croce d'Aune, Chorus, and later Athena) levers, there isn't a grub screw. The hinge pin, instead of being a straight cylindrical pin, has a pair of grooves cut around it -- picture a tiny barbell, with a little bulge in the center of it. Instead of a grub screw to hold it in place, it is held in place by a metal plate with two small "hooks" which wrap partway around the grooves in the hinge-pin. This metal plate is held in place by the mounting bolt and clamp assembly. As long as the lever is mounted to the handlebar, the pin will not slide out (in addition to the fact that the pin fits very snugly in the lever body).
To remove the lever from the body, first loosen the mounting bolt and remove the lever body from the handlebar clamp. Now the metal plate with the hooks will be loose inside the lever body. Next, either pull back the rubber brake hood, or remove it altogether, so that the hinge-pin can be seen on both sides of the lever body. Next, you'll need some kind of tool that you can use to drive the pin out of the lever body -- I used what basically amounted to an old awl with the tip filed flat, and I tapped with a hammer to push the pin out. Like I said, it seems to fit pretty snugly.
I haven't yet tried to put it all back together, but I have a feeling it isn't going to be as easy as the NR/SR levers -- getting all the pieces back into place, and to stay in place while trying to tap the pin back into position, and to try doing it inside the lever body where it is pretty difficult to get your fingers in there -- it seems like much swearing will be involved.