I have similar issue as you do with my accord 2006 coupe. I brought to couple dealers and they said that it's the "ABS self test" more like BS to me...It makes noise when you are accel. from 1.8k-2.5k RPM and only at the accel. mode that you could hear the noise. If you cruising at that RPM range, you wouldn't hear the noise. It does irritate the hell out of me too, but there's nothing you can do except turn on the music a little bit louder. Not a lot people got this problem, we are special!!!!
Another one for you....
My car keep on steering to the right within 6sec from center-to-center. IT'S FOR MY SAFETY?...that's what the Dealer tech. told me....
For both issues, there nothing they can do. As for me, this the first and last accord i buy

 

i've always heard a clicking noise on my fuel injected hondas...didnt notice it on my 88

 

you can hear it when u r driving? or u just rev the engine in order to hear it? Mine prob. happens only when driving. even sometime at 60-80mile/hr, i can still hear it.

 

if i listen really closely it is there...i just figured it was the valves....can i hear it over the radio with the windows closed? no.