Will a 120W PicoPSU and 120W adapter be enough to power this machine, at sustained levels of moderate to high load?
The 2120T is potentially 35W. Add another potential 25 to 40 watts for the board. See:http://www.silentpcreview.com/article1200-page5.html
You are up to 75 watts. While the advice others have given you is valid, you indicated is was sound, not power that was your primary concern.
I would use a 120W PicoPSU for a margin of safety. It will likely deliver perhaps 100 watts. That extra capacity will be a handy safety margin in the event you in the event that a run away process inadvertantly loads your computer to 100% over night when you aren't looking.
I would also consider the largest SPCR approved heatsink you can find that will fit easily in your case, and use it with a single 500 rpm Scythe Slipstream. Or a Scythe mugen 2 with it standard PWM slipstream would be cost effective. The fan will never tick past 300 rpm. If you are tight for space, any of the downdraft Noctua, even the smallest, will work just fine as well.