Well, I just raised it to my face (mine is a II), holding my left eye over the focus window and the viewfinder window, and it seems to be fine using the CSEP-1, at least for my face (I have a narrow face). When your thumb is in the TU, it actually prevents the TU from poking you in the eye. The "depth" of the TU is actually shallower than the height of your nose, so the biggest issue is the distance from the right side of your nose to your left eye. When my eye is over the viewfinder window, my thumb rests right against the right side of my nose and it feels pretty comfortable. If you have a wider face, then your nose might prevent you from placing your left eye squarely over the viewfinder window. If you have a later model Barnack where the focus/viewfinder windows are closer together, this may not be a problem at all.
I don't have my TU 3 with me at the moment, but since its longer than the CSEP-1, it may be even better for left eye'd shooters, but I think a lot of it depends on the size of your face and your hands. The TU 3 would place you thumb pretty close to the edge of the camara, and this might be uncomfortable if you have large hands. The TU 3 also does not have an accessory cold shoe, so you would not be able to mount any viewfinders.