As MikeHunt79 said (like the name

), it is possible. Note that if you plan to do this, you will have to underclock your processor, or keep it at stock, or else the temps will go sky high (talking of which, I wouldn't run your voltage that high 24/7. 1.45-1.5 is considered maximum, and you will get 3GHz in around 1.4125V or so. An extra 0.15V for an extra 240MHz isn't a great compromise).
If you got good cooler and good case really that's not that big of a problem.
I remember once I was changing something at one of the PCs, older san diego, and I accidentaly stuck cable into the poor zalman and the fan didnt even move which I didnt notice

, the CPU was running benchmarks full loaded and OCed with passive cooling for 1,5hr , the temps went to just 70c, and thats with not best cooler.
Anyways, back to OP questions.
For the totally silent system I would reccomend you the following:
Antec P182-P190 case, p190 even tho is a monster, will be obviously better choice for passive/silent cooling.
You can slap TRUE with some very low rpm (400-800) on it or leave it passive. Also, if you're crazy, you can get Scythe Orochi

and leave it passive

without fan !

.
You can cooler the GPU very well passively with accelero s1.
And maybe just get 2 very silent low rpm maybe 600rpm fans for case to get some airflow for the passive GPU/CPU coolers.
On the PSU aspect, most of the good PSUs for 70+ from thermaltake, seasonic, tagan or zalman are very silent and in P182/P190 you wont be able to hear them.
Lastly you can also quiet down your HDDs as well with the Zalman cooler
http://www.overclockers.co.uk/showproduct.php?prodid=SY-006-ZA
So zalman hdd cooler, true/orochi , 400-600rpm noctuas , accelero s1 + antec p182 - p190 = dead silent system

. This will be bit expensive but completely silent and effective, you even should be able to get decent OC.