How are you planning to connect the water and drain of the dishwasher if you put the plumbing behind it? What if your dishwasher is leaking and you want to shut it off? Pretty sure that the valve for the appliance has to be accessible.
99% of the time people aren't using their sink at the same time the dishwasher is running. If you think about it, you usually only run the dishwasher after the dishes are done, don't you?
As far as noise, i'd venture to guess that the noise that the motor in the dishwasher makes is louder than the water discharging into the sink drain for the 5 minutes that it's actually on the pumping out cycle.
I'd say conventional hookup is best. It really isn't that much more stuff under the sink anyway.