Definitely not inconspicuous, and less so with a big white lens attached. However, it has Silent Single Shooting mode, which is pretty quiet. It is much less intrusive than the shutter on my Rebel T2i. The 1Ds Mk III and 5D Mk III also have that mode. It separates the mirror slap and shutter sounds, plus being in a heavier weather sealed body doesn’t hurt. Even in regular mode, it seems quieter than the smaller cameras.
The 1Dx is about a stop better than the 5D Mk III for high ISO noise, which in a dark church or reception hall may really be a blessing, though I chose the 5D Mk III for the smaller size, larger pixel count and lower price tag. I don’t need it’s high frame rate, and auto-focus is the same, so I kept my 1Ds as a backup and got the 5D for when I need higher ISO and more ability than my Rebel.