Well, basically it depends on what you consider quiet. I used one of my WSPs as a webserver for over a year. I just took it offline a week ago, to upgrade to a faster server. I removed the original heatsink and put a much larger one on, with a much quieter fan. I also used a laptop harddrive. The noise coming from it was mostly harddrive noise, which was still pretty quiet. A standard harddrive would be a bit noisier depending on the model.
If you don't already have a websurfer, I would suggest a cheap minitower as a small home server. Configuration would be much easier and probably much cheaper. You can always put it in a closet if the noise bothers you.
Another thing is that if you are buying thhis from Allwell directly, it uses a heat pipe to remove processor heat. There aren't any fans in the Allwell box. So then all you would have to deal with is harddrive noise. But like I said above the Allwell box is pretty expensive and limited for a home server.