Yes. Live view can't function without the mirror being locked up.
In terms of reducing vibration, live view is even better than normal mirror lock-up as the camera then operates with an electronic first curtain so there is zero movement/vibration until the shutter closes mechanically. I'm 99% certain this is true of the 5D3, certainly is of the 5D2.
The 5D3's quiet shutter mode is also very good for reducing vibration. It works by slowing the mirror up/down, reducing noise and also vibration at the same time.