It's not as quick as a 1Ds2, but there's alot more mass to move (larger mirror, larger curtains, etc). With a Phase One back there is a shutter latency (short or long) option; short is the correct setting on the AFD II w/ focal plane shutter / lenses. I think some of the lag time is added with the back; a couple text strings cycle through the viewfinder - one of them being "DB CAP", but I think there is a message before that. My point is, getting the back ready to go may be adding some milliseconds to the equation.
There are probably some custom functions on the body which may influence things too - such as metering options. I remember changing a metering option which was supposed to extend battery life. If you're using AF focus, that'll slow things down since the camera locks focus first. There's no a beep, so sometimes I think it should just fire, but the camera is still tweaking focus in a very small adjustments.