First thing I do with a new camera is turn off all beeps. My camera is as quiet as I can get it. And I don't use a flash as a rule. Still, the mirror and shutter clacking is annoying enough if the venue is otherwise quiet. I don't envy wedding photographers, though (for many reasons). They must constantly be torn between getting that perfect shot and being a perfect pest.
The 6D silent mode sounds considerably quieter than my 7D, but it's still not silent by any means. Maybe this is where a good mirrorless rig would come in handy.
I have to admit, I don't know why there can't be an electronic 1st & 2nd curtain in live view. I am sure there is a reason, but that would be the really quite way to go, the 5dIII is pretty quite - not silent but quite.