Long as you're not putting in any traditional technology hard drives or removable media devices, you can get pretty close.
Your only real problem at that point will be the power supply, imho.
I live in a studio apartment, and try to make my computers pretty quiet. Thing is, fan noise is generally white noise, long as it isn't really loud, it fades into the background once you're used to it. Hard disk access noise and cd/dvd spin up noise, on the other hand is intermittant and can drive you crazy.
I was waking up at 3am every morning and couldn't figure out why, until I realized that was when my daily full antivirus scan kicked off. Those drives churning away were enough to wake me up every time. I just leave my pc on pretty much 24x7 nowadays and just have it do the av scan when I'm at work, not when I'm at home using the pc, or at home sleeping.