Im not sure breathable is a very well defined term; but if you want to get technical about it; yeah there is a difference between convection, as you would get from bulk a bulk gas being pumped around, versus molecular diffusion through the material. Subjectively the net result is the same though; how fast does a given amount of moisture go from one side to the other, and how much moisture will build up inside the shoe.
While a solid piece of leather technically is porous, the holes are so tiny that I think the amount of bulk convection through an unbroken piece of leather can be ignored. The way water gets through then, is by dissolving into the leather, diffusing along the leather fibers, and evaporating out at the other end. Same with PVAc; its a solid sheet of rubber without holes, but its a very hydrophilic rubber so water can diffuse through it. Hopefully fast enough to make a difference. Something like neophrene is super hydrophopic though; close to zero water molecules will dissolve into a rubber like that, and close to zero will make it to the other side.