C-3 has a leaf shutter, somewhat in front of the focal plane. I am not at home with a C3 to measure
I mounted a pinhole on a Deckel mount from a broken Kodak Retina Reflex lens and installed it like a lens. I think it was 41.5 mm in my case (ended up slightly recessed, I guess). The camera flange distance is 44.7 mm. Coverage and angle of view were 'normal', and I never noticed (nor expected) light falloff at that distance. The problem with this configuration is that I could never do a wide angle. The mirror was not a problem in the 'mount in front of shutter' configuration.
See the link below for others.
Dead Link Removed
Maybe I misunderstood your comment on distance from the film plane.
Nearly all SLR lenses are 'retrofocus' so, for example, a 200 mm lens need not be 200 mm from the film plane at infinity focus (as it need be in a view camera with a non-zoom lens).
I would assume the standard 50 mm lens on a C3 is not retrofocus. I don't know the lens flange distance but would assume it is 50 mm minus the distance from the flange mount to the relevant lens node (1. I don't know which one is important 2. Far easier to just measure the flange to film plane distance and note that it is probably less than the lens f.l.). Actually, looking at the referenced link above, there are some flange distances on some RF's that are shorter than typical SLR's.
Contax RF is 34.85 mm
Canon screw mount 28.8
Leica screw mount 28.8
Narcissus (here's lookin' at you) 28.8
So if Argus was thinking at all like everyone else, it may be on the order of 29 mm.
You could possibly (probably) accomplish a wide angle camera construction with a short flange distance RF, depending on the location of the pinhole vs. the shutter.
I once converted a Kodak 35 RF with a bad lens. When I was done I had a bad shutter too. I used aggressive double stick tape and slipped and got some on the shutter. Initially I left the lens body intact for looks, but it created a round image. I later took the lens barrel off and used a refrigerator magnet for a shutter after gluing a metal ring on the camera.