I'm not the most qualified to answer this question but here is what I would say:
First, everything has noise. Resistors, caps, wires, solder joints, etc. all have some noise even if it is virtually imperceptible. So, in that sense, I suppose that even a battery will exhibit some noise.
That being said, anything else you use to provide power will almost certainly have at least that amount of noise, plus other issues like ripple, spikes, and other fluctuations that won't be an issue with batteries.
Also, since there are many different types of batteries, I suppose some would have more noise than others. But again, for the smoothest DC around. The battery will be the way to go.
You probably get as much noise from solar flares and cosmic background radiation as you do from the batteries in a Quickie.